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

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

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

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

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

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

Combine like terms: -7x + 6x = -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}