(x-1)(x-2)=20

Solution for (x-1)(x-2)=20 equation:

Simplifying
(x + -1)(x + -2) = 20

Reorder the terms:
(-1 + x)(x + -2) = 20

Reorder the terms:
(-1 + x)(-2 + x) = 20

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) = 20
((-2 * -1 + x * -1) + x(-2 + x)) = 20
((2 + -1x) + x(-2 + x)) = 20
(2 + -1x + (-2 * x + x * x)) = 20
(2 + -1x + (-2x + x2)) = 20

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) = 20

Solving
2 + -3x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
2 + -20 + -3x + x2 = 20 + -20

Combine like terms: 2 + -20 = -18
-18 + -3x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}