(x-1)(x+1)=(x-5)(x+9)

Solution for (x-1)(x+1)=(x-5)(x+9) equation:

Simplifying
(x + -1)(x + 1) = (x + -5)(x + 9)

Reorder the terms:
(-1 + x)(x + 1) = (x + -5)(x + 9)

Reorder the terms:
(-1 + x)(1 + x) = (x + -5)(x + 9)

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) = (x + -5)(x + 9)
((1 * -1 + x * -1) + x(1 + x)) = (x + -5)(x + 9)
((-1 + -1x) + x(1 + x)) = (x + -5)(x + 9)
(-1 + -1x + (1 * x + x * x)) = (x + -5)(x + 9)
(-1 + -1x + (1x + x2)) = (x + -5)(x + 9)

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) = (x + -5)(x + 9)
(-1 + x2) = (x + -5)(x + 9)

Reorder the terms:
-1 + x2 = (-5 + x)(x + 9)

Reorder the terms:
-1 + x2 = (-5 + x)(9 + x)

Multiply (-5 + x) * (9 + x)
-1 + x2 = (-5(9 + x) + x(9 + x))
-1 + x2 = ((9 * -5 + x * -5) + x(9 + x))
-1 + x2 = ((-45 + -5x) + x(9 + x))
-1 + x2 = (-45 + -5x + (9 * x + x * x))
-1 + x2 = (-45 + -5x + (9x + x2))

Combine like terms: -5x + 9x = 4x
-1 + x2 = (-45 + 4x + x2)

Add '-1x2' to each side of the equation.
-1 + x2 + -1x2 = -45 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + 0 = -45 + 4x + x2 + -1x2
-1 = -45 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 = -45 + 4x + 0
-1 = -45 + 4x

Solving
-1 = -45 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
-1 + -4x = -45 + 4x + -4x

Combine like terms: 4x + -4x = 0
-1 + -4x = -45 + 0
-1 + -4x = -45

Add '1' to each side of the equation.
-1 + 1 + -4x = -45 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = -45 + 1
-4x = -45 + 1

Combine like terms: -45 + 1 = -44
-4x = -44

Divide each side by '-4'.
x = 11

Simplifying
x = 11