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

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


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

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

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

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

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

Solving
-1x + 36x3 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
x((1 + 6x)(-1 + 6x)) = 0

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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