(w-6)*(w-6)=25

Solution for (w-6)*(w-6)=25 equation:

Simplifying
(w + -6)(w + -6) = 25

Reorder the terms:
(-6 + w)(w + -6) = 25

Reorder the terms:
(-6 + w)(-6 + w) = 25

Multiply (-6 + w) * (-6 + w)
(-6(-6 + w) + w(-6 + w)) = 25
((-6 * -6 + w * -6) + w(-6 + w)) = 25
((36 + -6w) + w(-6 + w)) = 25
(36 + -6w + (-6 * w + w * w)) = 25
(36 + -6w + (-6w + w2)) = 25

Combine like terms: -6w + -6w = -12w
(36 + -12w + w2) = 25

Solving
36 + -12w + w2 = 25

Solving for variable 'w'.

Reorder the terms:
36 + -25 + -12w + w2 = 25 + -25

Combine like terms: 36 + -25 = 11
11 + -12w + w2 = 25 + -25

Combine like terms: 25 + -25 = 0
11 + -12w + w2 = 0

Factor a trinomial.
(1 + -1w)(11 + -1w) = 0

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve:

Simplifying
11 + -1w = 0

Solving
11 + -1w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1w = 0 + -11
-1w = 0 + -11

Combine like terms: 0 + -11 = -11
-1w = -11

Divide each side by '-1'.
w = 11

Simplifying
w = 11
Solution
w = {1, 11}