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

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

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

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

Multiply (-4 + x) * (6 + -3x)
6(-4(6 + -3x) + x(6 + -3x)) = 0
6((6 * -4 + -3x * -4) + x(6 + -3x)) = 0
6((-24 + 12x) + x(6 + -3x)) = 0
6(-24 + 12x + (6 * x + -3x * x)) = 0
6(-24 + 12x + (6x + -3x2)) = 0

Combine like terms: 12x + 6x = 18x
6(-24 + 18x + -3x2) = 0
(-24 * 6 + 18x * 6 + -3x2 * 6) = 0
(-144 + 108x + -18x2) = 0

Solving
-144 + 108x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-8 + 6x + -1x2) = 0

Factor a trinomial.
18((-4 + x)(2 + -1x)) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {4, 2}