x(6x-1)3(6x+1)=0

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Solution for x(6x-1)3(6x+1)=0 equation: 


Simplifying
x(6x + -1) * 3(6x + 1) = 0

Reorder the terms:
x(-1 + 6x) * 3(6x + 1) = 0

Reorder the terms:
x(-1 + 6x) * 3(1 + 6x) = 0

Reorder the terms for easier multiplication:
3x(-1 + 6x)(1 + 6x) = 0

Multiply (-1 + 6x) * (1 + 6x)
3x(-1(1 + 6x) + 6x * (1 + 6x)) = 0
3x((1 * -1 + 6x * -1) + 6x * (1 + 6x)) = 0
3x((-1 + -6x) + 6x * (1 + 6x)) = 0
3x(-1 + -6x + (1 * 6x + 6x * 6x)) = 0
3x(-1 + -6x + (6x + 36x2)) = 0

Combine like terms: -6x + 6x = 0
3x(-1 + 0 + 36x2) = 0
3x(-1 + 36x2) = 0
(-1 * 3x + 36x2 * 3x) = 0
(-3x + 108x3) = 0

Solving
-3x + 108x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1 + 36x2) = 0

Factor a difference between two squares.
3x((1 + 6x)(-1 + 6x)) = 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 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x = 0 + -1
6x = 0 + -1

Combine like terms: 0 + -1 = -1
6x = -1

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

Subproblem 3
Set the factor '(-1 + 6x)' equal to zero and attempt to solve:

Simplifying
-1 + 6x = 0

Solving
-1 + 6x = 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 + 6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6x = 0 + 1
6x = 0 + 1

Combine like terms: 0 + 1 = 1
6x = 1

Divide each side by '6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {0, -0.1666666667, 0.1666666667}

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