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

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

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

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

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

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

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

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

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

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

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

Solving
4x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, -4}