-w^2=36-12w

Solution for -w^2=36-12w equation:

Simplifying
-1w2 = 36 + -12w

Solving
-1w2 = 36 + -12w

Solving for variable 'w'.

Reorder the terms:
-36 + 12w + -1w2 = 36 + -12w + -36 + 12w

Reorder the terms:
-36 + 12w + -1w2 = 36 + -36 + -12w + 12w

Combine like terms: 36 + -36 = 0
-36 + 12w + -1w2 = 0 + -12w + 12w
-36 + 12w + -1w2 = -12w + 12w

Combine like terms: -12w + 12w = 0
-36 + 12w + -1w2 = 0

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

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

Simplifying
-6 + w = 0

Solving
-6 + w = 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 + w = 0 + 6

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

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

Simplifying
w = 6
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 = {6, 6}