(x-5)(x+13)=-80

Solution for (x-5)(x+13)=-80 equation:

Simplifying
(x + -5)(x + 13) = -80

Reorder the terms:
(-5 + x)(x + 13) = -80

Reorder the terms:
(-5 + x)(13 + x) = -80

Multiply (-5 + x) * (13 + x)
(-5(13 + x) + x(13 + x)) = -80
((13 * -5 + x * -5) + x(13 + x)) = -80
((-65 + -5x) + x(13 + x)) = -80
(-65 + -5x + (13 * x + x * x)) = -80
(-65 + -5x + (13x + x2)) = -80

Combine like terms: -5x + 13x = 8x
(-65 + 8x + x2) = -80

Solving
-65 + 8x + x2 = -80

Solving for variable 'x'.

Reorder the terms:
-65 + 80 + 8x + x2 = -80 + 80

Combine like terms: -65 + 80 = 15
15 + 8x + x2 = -80 + 80

Combine like terms: -80 + 80 = 0
15 + 8x + x2 = 0

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

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Subproblem 2
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
Solution
x = {-5, -3}