(2x-6)(x-3)=0

Solution for (2x-6)(x-3)=0 equation:

Simplifying
(2x + -6)(x + -3) = 0

Reorder the terms:
(-6 + 2x)(x + -3) = 0

Reorder the terms:
(-6 + 2x)(-3 + x) = 0

Multiply (-6 + 2x) * (-3 + x)
(-6(-3 + x) + 2x * (-3 + x)) = 0
((-3 * -6 + x * -6) + 2x * (-3 + x)) = 0
((18 + -6x) + 2x * (-3 + x)) = 0
(18 + -6x + (-3 * 2x + x * 2x)) = 0
(18 + -6x + (-6x + 2x2)) = 0

Combine like terms: -6x + -6x = -12x
(18 + -12x + 2x2) = 0

Solving
18 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -6x + x2) = 0

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

Ignore the factor 2.
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 '(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
Solution
x = {3, 3}