(x-3)(6x-18)=0

Solution for (x-3)(6x-18)=0 equation:

Simplifying
(x + -3)(6x + -18) = 0

Reorder the terms:
(-3 + x)(6x + -18) = 0

Reorder the terms:
(-3 + x)(-18 + 6x) = 0

Multiply (-3 + x) * (-18 + 6x)
(-3(-18 + 6x) + x(-18 + 6x)) = 0
((-18 * -3 + 6x * -3) + x(-18 + 6x)) = 0
((54 + -18x) + x(-18 + 6x)) = 0
(54 + -18x + (-18 * x + 6x * x)) = 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}