(x-8)(x-8)-81=0

Solution for (x-8)(x-8)-81=0 equation:

Simplifying
(x + -8)(x + -8) + -81 = 0

Reorder the terms:
(-8 + x)(x + -8) + -81 = 0

Reorder the terms:
(-8 + x)(-8 + x) + -81 = 0

Multiply (-8 + x) * (-8 + x)
(-8(-8 + x) + x(-8 + x)) + -81 = 0
((-8 * -8 + x * -8) + x(-8 + x)) + -81 = 0
((64 + -8x) + x(-8 + x)) + -81 = 0
(64 + -8x + (-8 * x + x * x)) + -81 = 0
(64 + -8x + (-8x + x2)) + -81 = 0

Combine like terms: -8x + -8x = -16x
(64 + -16x + x2) + -81 = 0

Reorder the terms:
64 + -81 + -16x + x2 = 0

Combine like terms: 64 + -81 = -17
-17 + -16x + x2 = 0

Solving
-17 + -16x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(17 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-1, 17}