(x-10)(x-10)=(x+10)

Solution for (x-10)(x-10)=(x+10) equation:

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

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

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

Multiply (-10 + x) * (-10 + x)
(-10(-10 + x) + x(-10 + x)) = (x + 10)
((-10 * -10 + x * -10) + x(-10 + x)) = (x + 10)
((100 + -10x) + x(-10 + x)) = (x + 10)
(100 + -10x + (-10 * x + x * x)) = (x + 10)
(100 + -10x + (-10x + x2)) = (x + 10)

Combine like terms: -10x + -10x = -20x
(100 + -20x + x2) = (x + 10)

Reorder the terms:
100 + -20x + x2 = (10 + x)

Remove parenthesis around (10 + x)
100 + -20x + x2 = 10 + x

Solving
100 + -20x + x2 = 10 + x

Solving for variable 'x'.

Reorder the terms:
100 + -10 + -20x + -1x + x2 = 10 + x + -10 + -1x

Combine like terms: 100 + -10 = 90
90 + -20x + -1x + x2 = 10 + x + -10 + -1x

Combine like terms: -20x + -1x = -21x
90 + -21x + x2 = 10 + x + -10 + -1x

Reorder the terms:
90 + -21x + x2 = 10 + -10 + x + -1x

Combine like terms: 10 + -10 = 0
90 + -21x + x2 = 0 + x + -1x
90 + -21x + x2 = x + -1x

Combine like terms: x + -1x = 0
90 + -21x + x2 = 0

Factor a trinomial.
(6 + -1x)(15 + -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 '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {6, 15}