Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "q2"  was replaced by  "q^2".  1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
      2
 ((9•(q2))-(—•(3q-7)))+5q2
      3
STEP
2
:
      2
Simplify  —
      3
Equation at the end of step
2
:
         2         Â
 ((9 • (q2)) -  (— • (3q - 7))) +  5q2
         3         Â
STEP
3
:
Equation at the end of step 3
        2 • (3q - 7)   Â
 ((9 • (q2)) -  ————————————) +  5q2
           3      Â
STEP Â
4
:
Equation at the end of step
4
:
     2 • (3q - 7)   Â
 (32q2 -  ————————————) +  5q2
        3      Â
STEP
5
:
Rewriting the whole as an Equivalent Fraction
5.1 Â Subtracting a fraction from a whole
Rewrite the whole as a fraction using  3  as the denominator :
      32q2   32q2 • 3
  32q2 =  ————  =  ————————
       1      3  Â
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
5.2 Â Â Â Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
32q2 • 3 - (2 • (3q-7))   27q2 - 6q + 14
———————————————————————  =  ——————————————
      3            3    Â
Equation at the end of step
5
:
 (27q2 - 6q + 14)  Â
 ———————————————— +  5q2
    3      Â
STEP
6
:
Rewriting the whole as an Equivalent Fraction :
6.1 Â Adding a whole to a fraction
Rewrite the whole as a fraction using  3  as the denominator :
     5q2   5q2 • 3
  5q2 =  ———  =  ———————
      1     3  Â
Trying to factor by splitting the middle term
6.2   Factoring  27q2 - 6q + 14 Â
The first term is,  27q2  its coefficient is  27 .
The middle term is,  -6q  its coefficient is  -6 .
The last term, "the constant", is  +14 Â
Step-1 : Multiply the coefficient of the first term by the constant  27 • 14 = 378 Â
Step-2 : Find two factors of  378  whose sum equals the coefficient of the middle term, which is  -6 .
   -378   +   -1   =   -379 Â
   -189   +   -2   =   -191 Â
   -126   +   -3   =   -129 Â
   -63   +   -6   =   -69 Â
   -54   +   -7   =   -61 Â
   -42   +   -9   =   -51 Â
For tidiness, printing of 26 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
6.3 Â Â Â Adding up the two equivalent fractions
(27q2-6q+14) + 5q2 • 3   42q2 - 6q + 14
——————————————————————  =  ——————————————
     3            3    Â
STEP
7
:
Pulling out like terms :
7.1 Â Â Pull out like factors :
 42q2 - 6q + 14  =  2 • (21q2 - 3q + 7) Â
Trying to factor by splitting the middle term
7.2   Factoring  21q2 - 3q + 7 Â
The first term is,  21q2  its coefficient is  21 .
The middle term is,  -3q  its coefficient is  -3 .
The last term, "the constant", is  +7 Â
Step-1 : Multiply the coefficient of the first term by the constant  21 • 7 = 147 Â
Step-2 : Find two factors of  147  whose sum equals the coefficient of the middle term, which is  -3 .
   -147   +   -1   =   -148 Â
   -49   +   -3   =   -52 Â
   -21   +   -7   =   -28 Â
   -7   +   -21   =   -28 Â
   -3   +   -49   =   -52 Â
   -1   +   -147   =   -148 Â
   1   +   147   =   148 Â
   3   +   49   =   52 Â
   7   +   21   =   28 Â
   21   +   7   =   28 Â
   49   +   3   =   52 Â
   147   +   1   =   148 Â
Observation : No two such factors can be found !!
Conclusion : Trinomial cannot be factored
Final result :
 2 • (21q2 - 3q + 7)
 ———————————————————
     3    Â