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

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


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

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

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

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

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

Reorder the terms:
1 + 2x + x2 = (-1 + x)(x + 5)

Reorder the terms:
1 + 2x + x2 = (-1 + x)(5 + x)

Multiply (-1 + x) * (5 + x)
1 + 2x + x2 = (-1(5 + x) + x(5 + x))
1 + 2x + x2 = ((5 * -1 + x * -1) + x(5 + x))
1 + 2x + x2 = ((-5 + -1x) + x(5 + x))
1 + 2x + x2 = (-5 + -1x + (5 * x + x * x))
1 + 2x + x2 = (-5 + -1x + (5x + x2))

Combine like terms: -1x + 5x = 4x
1 + 2x + x2 = (-5 + 4x + x2)

Add '-1x2' to each side of the equation.
1 + 2x + x2 + -1x2 = -5 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x + 0 = -5 + 4x + x2 + -1x2
1 + 2x = -5 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x = -5 + 4x + 0
1 + 2x = -5 + 4x

Solving
1 + 2x = -5 + 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 + 2x + -4x = -5 + 4x + -4x

Combine like terms: 2x + -4x = -2x
1 + -2x = -5 + 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -2x = -5 + 0
1 + -2x = -5

Add '-1' to each side of the equation.
1 + -1 + -2x = -5 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = -5 + -1
-2x = -5 + -1

Combine like terms: -5 + -1 = -6
-2x = -6

Divide each side by '-2'.
x = 3

Simplifying
x = 3

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