3w^2+3w=126

Solution for 3w^2+3w=126 equation:

Simplifying
3w2 + 3w = 126

Reorder the terms:
3w + 3w2 = 126

Solving
3w + 3w2 = 126

Solving for variable 'w'.

Reorder the terms:
-126 + 3w + 3w2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 3w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + w + w2) = 0

Factor a trinomial.
3((-7 + -1w)(6 + -1w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-7, 6}