2x(x-6)=x-20

Solution for 2x(x-6)=x-20 equation:

Simplifying
2x(x + -6) = x + -20

Reorder the terms:
2x(-6 + x) = x + -20
(-6 * 2x + x * 2x) = x + -20
(-12x + 2x2) = x + -20

Reorder the terms:
-12x + 2x2 = -20 + x

Solving
-12x + 2x2 = -20 + x

Solving for variable 'x'.

Reorder the terms:
20 + -12x + -1x + 2x2 = -20 + x + 20 + -1x

Combine like terms: -12x + -1x = -13x
20 + -13x + 2x2 = -20 + x + 20 + -1x

Reorder the terms:
20 + -13x + 2x2 = -20 + 20 + x + -1x

Combine like terms: -20 + 20 = 0
20 + -13x + 2x2 = 0 + x + -1x
20 + -13x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
20 + -13x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(4 + -1x) = 0

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Subproblem 2
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
Solution
x = {2.5, 4}