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

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

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

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

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

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

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

Reorder the terms:
-5 + 4x + x2 = (1 + x)(x + 1)

Reorder the terms:
-5 + 4x + x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
-5 + 4x + x2 = (1(1 + x) + x(1 + x))
-5 + 4x + x2 = ((1 * 1 + x * 1) + x(1 + x))
-5 + 4x + x2 = ((1 + 1x) + x(1 + x))
-5 + 4x + x2 = (1 + 1x + (1 * x + x * x))
-5 + 4x + x2 = (1 + 1x + (1x + x2))

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

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

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

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

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

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

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

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

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

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

Divide each side by '2'.
x = 3

Simplifying
x = 3