(2x-6)(2-x)=0

Solution for (2x-6)(2-x)=0 equation:

Simplifying
(2x + -6)(2 + -1x) = 0

Reorder the terms:
(-6 + 2x)(2 + -1x) = 0

Multiply (-6 + 2x) * (2 + -1x)
(-6(2 + -1x) + 2x * (2 + -1x)) = 0
((2 * -6 + -1x * -6) + 2x * (2 + -1x)) = 0
((-12 + 6x) + 2x * (2 + -1x)) = 0
(-12 + 6x + (2 * 2x + -1x * 2x)) = 0
(-12 + 6x + (4x + -2x2)) = 0

Combine like terms: 6x + 4x = 10x
(-12 + 10x + -2x2) = 0

Solving
-12 + 10x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5x + -1x2) = 0

Factor a trinomial.
2((-3 + x)(2 + -1x)) = 0

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

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3
Subproblem 2
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
Solution
x = {3, 2}