(x+8)*(x-7)=-14

Solution for (x+8)*(x-7)=-14 equation:

Simplifying
(x + 8)(x + -7) = -14

Reorder the terms:
(8 + x)(x + -7) = -14

Reorder the terms:
(8 + x)(-7 + x) = -14

Multiply (8 + x) * (-7 + x)
(8(-7 + x) + x(-7 + x)) = -14
((-7 * 8 + x * 8) + x(-7 + x)) = -14
((-56 + 8x) + x(-7 + x)) = -14
(-56 + 8x + (-7 * x + x * x)) = -14
(-56 + 8x + (-7x + x2)) = -14

Combine like terms: 8x + -7x = 1x
(-56 + 1x + x2) = -14

Solving
-56 + 1x + x2 = -14

Solving for variable 'x'.

Reorder the terms:
-56 + 14 + 1x + x2 = -14 + 14

Combine like terms: -56 + 14 = -42
-42 + 1x + x2 = -14 + 14

Combine like terms: -14 + 14 = 0
-42 + 1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
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 = {-7, 6}