(x-6)(x+7)=14

Solution for (x-6)(x+7)=14 equation:

Simplifying
(x + -6)(x + 7) = 14

Reorder the terms:
(-6 + x)(x + 7) = 14

Reorder the terms:
(-6 + x)(7 + x) = 14

Multiply (-6 + x) * (7 + x)
(-6(7 + x) + x(7 + x)) = 14
((7 * -6 + x * -6) + x(7 + x)) = 14
((-42 + -6x) + x(7 + x)) = 14
(-42 + -6x + (7 * x + x * x)) = 14
(-42 + -6x + (7x + x2)) = 14

Combine like terms: -6x + 7x = 1x
(-42 + 1x + x2) = 14

Solving
-42 + 1x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-42 + -14 + 1x + x2 = 14 + -14

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

Combine like terms: 14 + -14 = 0
-56 + 1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(7 + -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 '(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
Solution
x = {-8, 7}