3x(x-8)(3x-1)=0

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Solution for 3x(x-8)(3x-1)=0 equation: 


Simplifying
3x(x + -8)(3x + -1) = 0

Reorder the terms:
3x(-8 + x)(3x + -1) = 0

Reorder the terms:
3x(-8 + x)(-1 + 3x) = 0

Multiply (-8 + x) * (-1 + 3x)
3x(-8(-1 + 3x) + x(-1 + 3x)) = 0
3x((-1 * -8 + 3x * -8) + x(-1 + 3x)) = 0
3x((8 + -24x) + x(-1 + 3x)) = 0
3x(8 + -24x + (-1 * x + 3x * x)) = 0
3x(8 + -24x + (-1x + 3x2)) = 0

Combine like terms: -24x + -1x = -25x
3x(8 + -25x + 3x2) = 0
(8 * 3x + -25x * 3x + 3x2 * 3x) = 0
(24x + -75x2 + 9x3) = 0

Solving
24x + -75x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(8 + -25x + 3x2) = 0

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

Ignore the factor 3.

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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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, 0.3333333333, 8}

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