6(3x-3)(x-4)=0

Solution for 6(3x-3)(x-4)=0 equation:

Simplifying
6(3x + -3)(x + -4) = 0

Reorder the terms:
6(-3 + 3x)(x + -4) = 0

Reorder the terms:
6(-3 + 3x)(-4 + x) = 0

Multiply (-3 + 3x) * (-4 + x)
6(-3(-4 + x) + 3x * (-4 + x)) = 0
6((-4 * -3 + x * -3) + 3x * (-4 + x)) = 0
6((12 + -3x) + 3x * (-4 + x)) = 0
6(12 + -3x + (-4 * 3x + x * 3x)) = 0
6(12 + -3x + (-12x + 3x2)) = 0

Combine like terms: -3x + -12x = -15x
6(12 + -15x + 3x2) = 0
(12 * 6 + -15x * 6 + 3x2 * 6) = 0
(72 + -90x + 18x2) = 0

Solving
72 + -90x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(4 + -5x + x2) = 0

Factor a trinomial.
18((1 + -1x)(4 + -1x)) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}