(3x-9)(2x-6)=0

Solution for (3x-9)(2x-6)=0 equation:

Simplifying
(3x + -9)(2x + -6) = 0

Reorder the terms:
(-9 + 3x)(2x + -6) = 0

Reorder the terms:
(-9 + 3x)(-6 + 2x) = 0

Multiply (-9 + 3x) * (-6 + 2x)
(-9(-6 + 2x) + 3x * (-6 + 2x)) = 0
((-6 * -9 + 2x * -9) + 3x * (-6 + 2x)) = 0
((54 + -18x) + 3x * (-6 + 2x)) = 0
(54 + -18x + (-6 * 3x + 2x * 3x)) = 0
(54 + -18x + (-18x + 6x2)) = 0

Combine like terms: -18x + -18x = -36x
(54 + -36x + 6x2) = 0

Solving
54 + -36x + 6x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
6((3 + -1x)(3 + -1x)) = 0

Ignore the factor 6.
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}