2w^2-6w=108

Solution for 2w^2-6w=108 equation:

Simplifying
2w2 + -6w = 108

Reorder the terms:
-6w + 2w2 = 108

Solving
-6w + 2w2 = 108

Solving for variable 'w'.

Reorder the terms:
-108 + -6w + 2w2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + -6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -3w + w2) = 0

Factor a trinomial.
2((-6 + -1w)(9 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {-6, 9}