What is the answer to 3w squared +14w+8=0

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

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