3w² + 14w + 8 = 0
Multiply first and last coefficients: 3*8 = 24
We look for two numbers that multiply to give 24, and add to give the middle coefficient +14
Those two numbers are 2 and 12.
Check: 2*12 = 24 2 + 12 = 14
We replace the middle term of 14w in the quadratic expression with 2w +12w
3w² + 14w + 8 = 0
3w² + 2w + 12w + 8 = 0
w(3w + 2) +4(3w + 2) = 0
(3w + 2)(w + 4) = 0
3w + 2 = 0 or w + 4 = 0
3w = 0 -2 w = 0 - 4
3w = -2 w = -4
w = -2/3
The solutions are w = -2/3 or -4