6(x*x*x)-36(x*x)+30x=0

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Solution for 6(x*x*x)-36(x*x)+30x=0 equation: 


Simplifying
6(x * x * x) + -36(x * x) + 30x = 0

Multiply x * x
6(x2 * x) + -36(x * x) + 30x = 0

Multiply x2 * x
6(x3) + -36(x * x) + 30x = 0

Multiply x * x
6x3 + -36(x2) + 30x = 0

Reorder the terms:
30x + -36x2 + 6x3 = 0

Solving
30x + -36x2 + 6x3 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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, 1, 5}

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