(x+13)(x-8)=-68

Solution for (x+13)(x-8)=-68 equation:

Simplifying
(x + 13)(x + -8) = -68

Reorder the terms:
(13 + x)(x + -8) = -68

Reorder the terms:
(13 + x)(-8 + x) = -68

Multiply (13 + x) * (-8 + x)
(13(-8 + x) + x(-8 + x)) = -68
((-8 * 13 + x * 13) + x(-8 + x)) = -68
((-104 + 13x) + x(-8 + x)) = -68
(-104 + 13x + (-8 * x + x * x)) = -68
(-104 + 13x + (-8x + x2)) = -68

Combine like terms: 13x + -8x = 5x
(-104 + 5x + x2) = -68

Solving
-104 + 5x + x2 = -68

Solving for variable 'x'.

Reorder the terms:
-104 + 68 + 5x + x2 = -68 + 68

Combine like terms: -104 + 68 = -36
-36 + 5x + x2 = -68 + 68

Combine like terms: -68 + 68 = 0
-36 + 5x + x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 4}