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

Solution for 0=(x+1)(x-5) equation:

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

Reorder the terms:
0 = (1 + x)(x + -5)

Reorder the terms:
0 = (1 + x)(-5 + x)

Multiply (1 + x) * (-5 + x)
0 = (1(-5 + x) + x(-5 + x))
0 = ((-5 * 1 + x * 1) + x(-5 + x))
0 = ((-5 + 1x) + x(-5 + x))
0 = (-5 + 1x + (-5 * x + x * x))
0 = (-5 + 1x + (-5x + x2))

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

Solving
0 = -5 + -4x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(5 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {5, -1}