x^2*(x+117)*(3x-9)=0

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Solution for x^2*(x+117)*(3x-9)=0 equation: 


Simplifying
x2(x + 117)(3x + -9) = 0

Reorder the terms:
x2(117 + x)(3x + -9) = 0

Reorder the terms:
x2(117 + x)(-9 + 3x) = 0

Multiply (117 + x) * (-9 + 3x)
x2(117(-9 + 3x) + x(-9 + 3x)) = 0
x2((-9 * 117 + 3x * 117) + x(-9 + 3x)) = 0
x2((-1053 + 351x) + x(-9 + 3x)) = 0
x2(-1053 + 351x + (-9 * x + 3x * x)) = 0
x2(-1053 + 351x + (-9x + 3x2)) = 0

Combine like terms: 351x + -9x = 342x
x2(-1053 + 342x + 3x2) = 0
(-1053 * x2 + 342x * x2 + 3x2 * x2) = 0
(-1053x2 + 342x3 + 3x4) = 0

Solving
-1053x2 + 342x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-351 + 114x + x2) = 0

Factor a trinomial.
3x2((-117 + -1x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-117 + -1x)' equal to zero and attempt to solve:

Simplifying
-117 + -1x = 0

Solving
-117 + -1x = 0

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

Add '117' to each side of the equation.
-117 + 117 + -1x = 0 + 117

Combine like terms: -117 + 117 = 0
0 + -1x = 0 + 117
-1x = 0 + 117

Combine like terms: 0 + 117 = 117
-1x = 117

Divide each side by '-1'.
x = -117

Simplifying
x = -117

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -117, 3}

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