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

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

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

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

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

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

Combine like terms: 7x + -5x = 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.
(-8 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-8, 6}