(x-5)(x+1)=-8

Solution for (x-5)(x+1)=-8 equation:

Simplifying
(x + -5)(x + 1) = -8

Reorder the terms:
(-5 + x)(x + 1) = -8

Reorder the terms:
(-5 + x)(1 + x) = -8

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x)) = -8
((1 * -5 + x * -5) + x(1 + x)) = -8
((-5 + -5x) + x(1 + x)) = -8
(-5 + -5x + (1 * x + x * x)) = -8
(-5 + -5x + (1x + x2)) = -8

Combine like terms: -5x + 1x = -4x
(-5 + -4x + x2) = -8

Solving
-5 + -4x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-5 + 8 + -4x + x2 = -8 + 8

Combine like terms: -5 + 8 = 3
3 + -4x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
3 + -4x + x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}