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

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

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

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

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

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

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

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

Solving
-1 + x2 = 5 + 5x

Solving for variable 'x'.

Reorder the terms:
-1 + -5 + -5x + x2 = 5 + 5x + -5 + -5x

Combine like terms: -1 + -5 = -6
-6 + -5x + x2 = 5 + 5x + -5 + -5x

Reorder the terms:
-6 + -5x + x2 = 5 + -5 + 5x + -5x

Combine like terms: 5 + -5 = 0
-6 + -5x + x2 = 0 + 5x + -5x
-6 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-6 + -5x + x2 = 0

Factor a trinomial.
(-1 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}