(2x-6)(3x-24)x=

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Solution for (2x-6)(3x-24)x= equation: 


Simplifying
(2x + -6)(3x + -24) * x = 0

Reorder the terms:
(-6 + 2x)(3x + -24) * x = 0

Reorder the terms:
(-6 + 2x)(-24 + 3x) * x = 0

Reorder the terms for easier multiplication:
x(-6 + 2x)(-24 + 3x) = 0

Multiply (-6 + 2x) * (-24 + 3x)
x(-6(-24 + 3x) + 2x * (-24 + 3x)) = 0
x((-24 * -6 + 3x * -6) + 2x * (-24 + 3x)) = 0
x((144 + -18x) + 2x * (-24 + 3x)) = 0
x(144 + -18x + (-24 * 2x + 3x * 2x)) = 0
x(144 + -18x + (-48x + 6x2)) = 0

Combine like terms: -18x + -48x = -66x
x(144 + -66x + 6x2) = 0
(144 * x + -66x * x + 6x2 * x) = 0
(144x + -66x2 + 6x3) = 0

Solving
144x + -66x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(24 + -11x + x2) = 0

Factor a trinomial.
6x((3 + -1x)(8 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 3, 8}

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