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

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

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

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

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

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

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

Reorder the terms:
-5 + 4x + x2 = 5 + x

Solving
-5 + 4x + x2 = 5 + x

Solving for variable 'x'.

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

Combine like terms: -5 + -5 = -10
-10 + 4x + -1x + x2 = 5 + x + -5 + -1x

Combine like terms: 4x + -1x = 3x
-10 + 3x + x2 = 5 + x + -5 + -1x

Reorder the terms:
-10 + 3x + x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-10 + 3x + x2 = 0 + x + -1x
-10 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

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

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

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}