(x+1)*(x-1)=(x-3)*(x+5)

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Solution for (x+1)*(x-1)=(x-3)*(x+5) equation: 


Simplifying
(x + 1)(x + -1) = (x + -3)(x + 5)

Reorder the terms:
(1 + x)(x + -1) = (x + -3)(x + 5)

Reorder the terms:
(1 + x)(-1 + x) = (x + -3)(x + 5)

Multiply (1 + x) * (-1 + x)
(1(-1 + x) + x(-1 + x)) = (x + -3)(x + 5)
((-1 * 1 + x * 1) + x(-1 + x)) = (x + -3)(x + 5)
((-1 + 1x) + x(-1 + x)) = (x + -3)(x + 5)
(-1 + 1x + (-1 * x + x * x)) = (x + -3)(x + 5)
(-1 + 1x + (-1x + x2)) = (x + -3)(x + 5)

Combine like terms: 1x + -1x = 0
(-1 + 0 + x2) = (x + -3)(x + 5)
(-1 + x2) = (x + -3)(x + 5)

Reorder the terms:
-1 + x2 = (-3 + x)(x + 5)

Reorder the terms:
-1 + x2 = (-3 + x)(5 + x)

Multiply (-3 + x) * (5 + x)
-1 + x2 = (-3(5 + x) + x(5 + x))
-1 + x2 = ((5 * -3 + x * -3) + x(5 + x))
-1 + x2 = ((-15 + -3x) + x(5 + x))
-1 + x2 = (-15 + -3x + (5 * x + x * x))
-1 + x2 = (-15 + -3x + (5x + x2))

Combine like terms: -3x + 5x = 2x
-1 + x2 = (-15 + 2x + x2)

Add '-1x2' to each side of the equation.
-1 + x2 + -1x2 = -15 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + 0 = -15 + 2x + x2 + -1x2
-1 = -15 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 = -15 + 2x + 0
-1 = -15 + 2x

Solving
-1 = -15 + 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.
-1 + -2x = -15 + 2x + -2x

Combine like terms: 2x + -2x = 0
-1 + -2x = -15 + 0
-1 + -2x = -15

Add '1' to each side of the equation.
-1 + 1 + -2x = -15 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = -15 + 1
-2x = -15 + 1

Combine like terms: -15 + 1 = -14
-2x = -14

Divide each side by '-2'.
x = 7

Simplifying
x = 7

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