(x-1)(x+5)+8=0

Solution for (x-1)(x+5)+8=0 equation:

Simplifying
(x + -1)(x + 5) + 8 = 0

Reorder the terms:
(-1 + x)(x + 5) + 8 = 0

Reorder the terms:
(-1 + x)(5 + x) + 8 = 0

Multiply (-1 + x) * (5 + x)
(-1(5 + x) + x(5 + x)) + 8 = 0
((5 * -1 + x * -1) + x(5 + x)) + 8 = 0
((-5 + -1x) + x(5 + x)) + 8 = 0
(-5 + -1x + (5 * x + x * x)) + 8 = 0
(-5 + -1x + (5x + x2)) + 8 = 0

Combine like terms: -1x + 5x = 4x
(-5 + 4x + x2) + 8 = 0

Reorder the terms:
-5 + 8 + 4x + x2 = 0

Combine like terms: -5 + 8 = 3
3 + 4x + x2 = 0

Solving
3 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + x)(1 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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