w^2=8w-12

Solution for w^2=8w-12 equation:

Simplifying
w2 = 8w + -12

Reorder the terms:
w2 = -12 + 8w

Solving
w2 = -12 + 8w

Solving for variable 'w'.

Reorder the terms:
12 + -8w + w2 = -12 + 8w + 12 + -8w

Reorder the terms:
12 + -8w + w2 = -12 + 12 + 8w + -8w

Combine like terms: -12 + 12 = 0
12 + -8w + w2 = 0 + 8w + -8w
12 + -8w + w2 = 8w + -8w

Combine like terms: 8w + -8w = 0
12 + -8w + w2 = 0

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

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
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 = {2, 6}