(x-2)(x-3)=20

Solution for (x-2)(x-3)=20 equation:

Simplifying
(x + -2)(x + -3) = 20

Reorder the terms:
(-2 + x)(x + -3) = 20

Reorder the terms:
(-2 + x)(-3 + x) = 20

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 20
((-3 * -2 + x * -2) + x(-3 + x)) = 20
((6 + -2x) + x(-3 + x)) = 20
(6 + -2x + (-3 * x + x * x)) = 20
(6 + -2x + (-3x + x2)) = 20

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 20

Solving
6 + -5x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
6 + -20 + -5x + x2 = 20 + -20

Combine like terms: 6 + -20 = -14
-14 + -5x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-14 + -5x + x2 = 0

Factor a trinomial.
(-2 + -1x)(7 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2, 7}