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

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

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

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

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

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

Combine like terms: -6x + -6x = -12x
3(18 + -12x + 2x2) = 0
(18 * 3 + -12x * 3 + 2x2 * 3) = 0
(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}