(w-12)*(w-12)=36

Solution for (w-12)*(w-12)=36 equation:

Simplifying
(w + -12)(w + -12) = 36

Reorder the terms:
(-12 + w)(w + -12) = 36

Reorder the terms:
(-12 + w)(-12 + w) = 36

Multiply (-12 + w) * (-12 + w)
(-12(-12 + w) + w(-12 + w)) = 36
((-12 * -12 + w * -12) + w(-12 + w)) = 36
((144 + -12w) + w(-12 + w)) = 36
(144 + -12w + (-12 * w + w * w)) = 36
(144 + -12w + (-12w + w2)) = 36

Combine like terms: -12w + -12w = -24w
(144 + -24w + w2) = 36

Solving
144 + -24w + w2 = 36

Solving for variable 'w'.

Reorder the terms:
144 + -36 + -24w + w2 = 36 + -36

Combine like terms: 144 + -36 = 108
108 + -24w + w2 = 36 + -36

Combine like terms: 36 + -36 = 0
108 + -24w + w2 = 0

Factor a trinomial.
(6 + -1w)(18 + -1w) = 0

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 '(18 + -1w)' equal to zero and attempt to solve:

Simplifying
18 + -1w = 0

Solving
18 + -1w = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1w = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1w = 0 + -18
-1w = 0 + -18

Combine like terms: 0 + -18 = -18
-1w = -18

Divide each side by '-1'.
w = 18

Simplifying
w = 18
Solution
w = {6, 18}