2x(x-6)=6-x

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

Simplifying
2x(x + -6) = 6 + -1x

Reorder the terms:
2x(-6 + x) = 6 + -1x
(-6 * 2x + x * 2x) = 6 + -1x
(-12x + 2x2) = 6 + -1x

Solving
-12x + 2x2 = 6 + -1x

Solving for variable 'x'.

Reorder the terms:
-6 + -12x + x + 2x2 = 6 + -1x + -6 + x

Combine like terms: -12x + x = -11x
-6 + -11x + 2x2 = 6 + -1x + -6 + x

Reorder the terms:
-6 + -11x + 2x2 = 6 + -6 + -1x + x

Combine like terms: 6 + -6 = 0
-6 + -11x + 2x2 = 0 + -1x + x
-6 + -11x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-6 + -11x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(6 + -1x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {-0.5, 6}