X^2+10z-96=0 i don’t get it

im only in 6th grade and i have no idea what type of math that is but i found this of a website, i dont know if this will help or not but i tried  

Factoring  x2-10x-96

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  -96

Step-1 : Multiply the coefficient of the first term by the constant   1 • -96 = -96

Step-2 : Find two factors of  -96  whose sum equals the coefficient of the middle term, which is   -10 .

     -96    +1    =  -95

     -48    +   2    =   -46

     -32    +   3    =   -29

     -24    +   4    =   -20

     -16    +   6    =   -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -16  and  6

                    x2 - 16x + 6x - 96

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-16)

             Add up the last 2 terms, pulling out common factors :

                   6 • (x-16)

Step-5 : Add up the four terms of step 4 :

                   (x+6)  •  (x-16)

            Which is the desired factorization

Equation at the end of step

1

:

 (x + 6) • (x - 16)  = 0

STEP

2

:

Theory - Roots of a product

2.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2      Solve  :    x+6 = 0

Subtract  6  from both sides of the equation :

                     x = -6

Solving a Single Variable Equation:

2.3      Solve  :    x-16 = 0

Add  16  to both sides of the equation :

                     x = 16

Supplement : Solving Quadratic Equation Directly

Solving    x2-10x-96  = 0   directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = x2-10x-96

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   5.0000  

Plugging into the parabola formula   5.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 5.00 * 5.00 - 10.0 * 5.00 - 96.0

or   y = -121.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-10x-96

Axis of Symmetry (dashed)  {x}={ 5.00}

Vertex at  {x,y} = { 5.00,-121.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-6.00, 0.00}

Root 2 at  {x,y} = {16.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2     Solving   x2-10x-96 = 0 by Completing The Square .

Add  96  to both side of the equation :

  x2-10x = 96

Now the clever bit: Take the coefficient of  x , which is  10 , divide by two, giving  5 , and finally square it giving  25

Add  25  to both sides of the equation :

 On the right hand side we have :

  96  +  25    or,  (96/1)+(25/1)

 The common denominator of the two fractions is  1   Adding  (96/1)+(25/1)  gives  121/1

 So adding to both sides we finally get :

  x2-10x+25 = 121

Adding  25  has completed the left hand side into a perfect square :

  x2-10x+25  =

  (x-5) • (x-5)  =

 (x-5)2

Things which are equal to the same thing are also equal to one another. Since

  x2-10x+25 = 121 and

  x2-10x+25 = (x-5)2

then, according to the law of transitivity,

  (x-5)2 = 121

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-5)2   is

  (x-5)2/2 =

 (x-5)1 =

  x-5

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-5 = √ 121

Add  5  to both sides to obtain:

  x = 5 + √ 121

Since a square root has two values, one positive and the other negative

  x2 - 10x - 96 = 0

  has two solutions:

 x = 5 + √ 121

  or

 x = 5 - √ 121

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.