(x-9)(x-3)=91

Solution for (x-9)(x-3)=91 equation:

Simplifying
(x + -9)(x + -3) = 91

Reorder the terms:
(-9 + x)(x + -3) = 91

Reorder the terms:
(-9 + x)(-3 + x) = 91

Multiply (-9 + x) * (-3 + x)
(-9(-3 + x) + x(-3 + x)) = 91
((-3 * -9 + x * -9) + x(-3 + x)) = 91
((27 + -9x) + x(-3 + x)) = 91
(27 + -9x + (-3 * x + x * x)) = 91
(27 + -9x + (-3x + x2)) = 91

Combine like terms: -9x + -3x = -12x
(27 + -12x + x2) = 91

Solving
27 + -12x + x2 = 91

Solving for variable 'x'.

Reorder the terms:
27 + -91 + -12x + x2 = 91 + -91

Combine like terms: 27 + -91 = -64
-64 + -12x + x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-64 + -12x + x2 = 0

Factor a trinomial.
(-4 + -1x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-4, 16}