What is the answer to 2x squared+ 7x+3=0

2x^2 + 7x + 3 = 0
(2x + 1)(x + 3) = 0

2x+1= 0 x + 3 = 0
2x = -1 x = -3
x = -1/2

x = -1/2 and -1

2x² + 7x + 3 = 0     

Multiply first and last coefficients:  2*3 = 6

We look for two numbers that multiply to give 6, and add to give 7

Those two numbers are 1 and 6.

Check:   6*1 = 6         6 + 1 = 7

We replace the middle term of +7x in the quadratic expression with 1x + 6x

 2x² + 7x + 3 = 0     

2x² + 1x + 6x + 3 = 0     

x(2x + 1) + 3(2x + 1) = 0

(2x + 1)(x +3) = 0

2x + 1 = 0    or  x + 3 = 0

2x = 0 -1              x = 0 - 3

2x = -1                 x = -3

x = -1/2

The solutions are x = -1/2  or  -3.