(x-4)(x+5)=-8

Solution for (x-4)(x+5)=-8 equation:

Simplifying
(x + -4)(x + 5) = -8

Reorder the terms:
(-4 + x)(x + 5) = -8

Reorder the terms:
(-4 + x)(5 + x) = -8

Multiply (-4 + x) * (5 + x)
(-4(5 + x) + x(5 + x)) = -8
((5 * -4 + x * -4) + x(5 + x)) = -8
((-20 + -4x) + x(5 + x)) = -8
(-20 + -4x + (5 * x + x * x)) = -8
(-20 + -4x + (5x + x2)) = -8

Combine like terms: -4x + 5x = 1x
(-20 + 1x + x2) = -8

Solving
-20 + 1x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-20 + 8 + 1x + x2 = -8 + 8

Combine like terms: -20 + 8 = -12
-12 + 1x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 3}