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.