(x-9)(x+9)=(x-1)(x-1)

Solution for (x-9)(x+9)=(x-1)(x-1) equation:

Simplifying
(x + -9)(x + 9) = (x + -1)(x + -1)

Reorder the terms:
(-9 + x)(x + 9) = (x + -1)(x + -1)

Reorder the terms:
(-9 + x)(9 + x) = (x + -1)(x + -1)

Multiply (-9 + x) * (9 + x)
(-9(9 + x) + x(9 + x)) = (x + -1)(x + -1)
((9 * -9 + x * -9) + x(9 + x)) = (x + -1)(x + -1)
((-81 + -9x) + x(9 + x)) = (x + -1)(x + -1)
(-81 + -9x + (9 * x + x * x)) = (x + -1)(x + -1)
(-81 + -9x + (9x + x2)) = (x + -1)(x + -1)

Combine like terms: -9x + 9x = 0
(-81 + 0 + x2) = (x + -1)(x + -1)
(-81 + x2) = (x + -1)(x + -1)

Reorder the terms:
-81 + x2 = (-1 + x)(x + -1)

Reorder the terms:
-81 + x2 = (-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
-81 + x2 = (-1(-1 + x) + x(-1 + x))
-81 + x2 = ((-1 * -1 + x * -1) + x(-1 + x))
-81 + x2 = ((1 + -1x) + x(-1 + x))
-81 + x2 = (1 + -1x + (-1 * x + x * x))
-81 + x2 = (1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
-81 + x2 = (1 + -2x + x2)

Add '-1x2' to each side of the equation.
-81 + x2 + -1x2 = 1 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-81 + 0 = 1 + -2x + x2 + -1x2
-81 = 1 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-81 = 1 + -2x + 0
-81 = 1 + -2x

Solving
-81 = 1 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
-81 + 2x = 1 + -2x + 2x

Combine like terms: -2x + 2x = 0
-81 + 2x = 1 + 0
-81 + 2x = 1

Add '81' to each side of the equation.
-81 + 81 + 2x = 1 + 81

Combine like terms: -81 + 81 = 0
0 + 2x = 1 + 81
2x = 1 + 81

Combine like terms: 1 + 81 = 82
2x = 82

Divide each side by '2'.
x = 41

Simplifying
x = 41