(x-5)(x-5)-10=111

Solution for (x-5)(x-5)-10=111 equation:

Simplifying
(x + -5)(x + -5) + -10 = 111

Reorder the terms:
(-5 + x)(x + -5) + -10 = 111

Reorder the terms:
(-5 + x)(-5 + x) + -10 = 111

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + -10 = 111
((-5 * -5 + x * -5) + x(-5 + x)) + -10 = 111
((25 + -5x) + x(-5 + x)) + -10 = 111
(25 + -5x + (-5 * x + x * x)) + -10 = 111
(25 + -5x + (-5x + x2)) + -10 = 111

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + -10 = 111

Reorder the terms:
25 + -10 + -10x + x2 = 111

Combine like terms: 25 + -10 = 15
15 + -10x + x2 = 111

Solving
15 + -10x + x2 = 111

Solving for variable 'x'.

Reorder the terms:
15 + -111 + -10x + x2 = 111 + -111

Combine like terms: 15 + -111 = -96
-96 + -10x + x2 = 111 + -111

Combine like terms: 111 + -111 = 0
-96 + -10x + x2 = 0

Factor a trinomial.
(-6 + -1x)(16 + -1x) = 0

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-6, 16}