(x-1)(x-10)=22

Solution for (x-1)(x-10)=22 equation:

Simplifying
(x + -1)(x + -10) = 22

Reorder the terms:
(-1 + x)(x + -10) = 22

Reorder the terms:
(-1 + x)(-10 + x) = 22

Multiply (-1 + x) * (-10 + x)
(-1(-10 + x) + x(-10 + x)) = 22
((-10 * -1 + x * -1) + x(-10 + x)) = 22
((10 + -1x) + x(-10 + x)) = 22
(10 + -1x + (-10 * x + x * x)) = 22
(10 + -1x + (-10x + x2)) = 22

Combine like terms: -1x + -10x = -11x
(10 + -11x + x2) = 22

Solving
10 + -11x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
10 + -22 + -11x + x2 = 22 + -22

Combine like terms: 10 + -22 = -12
-12 + -11x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-12 + -11x + x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
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 = {-1, 12}