(3x-9)x(2x-8)=0

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Solution for (3x-9)x(2x-8)=0 equation: 


Simplifying
(3x + -9) * x(2x + -8) = 0

Reorder the terms:
(-9 + 3x) * x(2x + -8) = 0

Reorder the terms:
(-9 + 3x) * x(-8 + 2x) = 0

Reorder the terms for easier multiplication:
x(-9 + 3x)(-8 + 2x) = 0

Multiply (-9 + 3x) * (-8 + 2x)
x(-9(-8 + 2x) + 3x * (-8 + 2x)) = 0
x((-8 * -9 + 2x * -9) + 3x * (-8 + 2x)) = 0
x((72 + -18x) + 3x * (-8 + 2x)) = 0
x(72 + -18x + (-8 * 3x + 2x * 3x)) = 0
x(72 + -18x + (-24x + 6x2)) = 0

Combine like terms: -18x + -24x = -42x
x(72 + -42x + 6x2) = 0
(72 * x + -42x * x + 6x2 * x) = 0
(72x + -42x2 + 6x3) = 0

Solving
72x + -42x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(12 + -7x + x2) = 0

Factor a trinomial.
6x((3 + -1x)(4 + -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 '(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 = {0, 3, 4}

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