x(x-5)(6x-1)=0

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Solution for x(x-5)(6x-1)=0 equation: 


Simplifying
x(x + -5)(6x + -1) = 0

Reorder the terms:
x(-5 + x)(6x + -1) = 0

Reorder the terms:
x(-5 + x)(-1 + 6x) = 0

Multiply (-5 + x) * (-1 + 6x)
x(-5(-1 + 6x) + x(-1 + 6x)) = 0
x((-1 * -5 + 6x * -5) + x(-1 + 6x)) = 0
x((5 + -30x) + x(-1 + 6x)) = 0
x(5 + -30x + (-1 * x + 6x * x)) = 0
x(5 + -30x + (-1x + 6x2)) = 0

Combine like terms: -30x + -1x = -31x
x(5 + -31x + 6x2) = 0
(5 * x + -31x * x + 6x2 * x) = 0
(5x + -31x2 + 6x3) = 0

Solving
5x + -31x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -31x + 6x2) = 0

Factor a trinomial.
x((1 + -6x)(5 + -1x)) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 0.1666666667, 5}

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