(x+6)(x-7)=90

Solution for (x+6)(x-7)=90 equation:

Simplifying
(x + 6)(x + -7) = 90

Reorder the terms:
(6 + x)(x + -7) = 90

Reorder the terms:
(6 + x)(-7 + x) = 90

Multiply (6 + x) * (-7 + x)
(6(-7 + x) + x(-7 + x)) = 90
((-7 * 6 + x * 6) + x(-7 + x)) = 90
((-42 + 6x) + x(-7 + x)) = 90
(-42 + 6x + (-7 * x + x * x)) = 90
(-42 + 6x + (-7x + x2)) = 90

Combine like terms: 6x + -7x = -1x
(-42 + -1x + x2) = 90

Solving
-42 + -1x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-42 + -90 + -1x + x2 = 90 + -90

Combine like terms: -42 + -90 = -132
-132 + -1x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-132 + -1x + x2 = 0

Factor a trinomial.
(-11 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-11, 12}