(x+5)(x-7)=13

Solution for (x+5)(x-7)=13 equation:

Simplifying
(x + 5)(x + -7) = 13

Reorder the terms:
(5 + x)(x + -7) = 13

Reorder the terms:
(5 + x)(-7 + x) = 13

Multiply (5 + x) * (-7 + x)
(5(-7 + x) + x(-7 + x)) = 13
((-7 * 5 + x * 5) + x(-7 + x)) = 13
((-35 + 5x) + x(-7 + x)) = 13
(-35 + 5x + (-7 * x + x * x)) = 13
(-35 + 5x + (-7x + x2)) = 13

Combine like terms: 5x + -7x = -2x
(-35 + -2x + x2) = 13

Solving
-35 + -2x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-35 + -13 + -2x + x2 = 13 + -13

Combine like terms: -35 + -13 = -48
-48 + -2x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}