(x-9)(3x+15)x=0

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Solution for (x-9)(3x+15)x=0 equation: 


Simplifying
(x + -9)(3x + 15) * x = 0

Reorder the terms:
(-9 + x)(3x + 15) * x = 0

Reorder the terms:
(-9 + x)(15 + 3x) * x = 0

Reorder the terms for easier multiplication:
x(-9 + x)(15 + 3x) = 0

Multiply (-9 + x) * (15 + 3x)
x(-9(15 + 3x) + x(15 + 3x)) = 0
x((15 * -9 + 3x * -9) + x(15 + 3x)) = 0
x((-135 + -27x) + x(15 + 3x)) = 0
x(-135 + -27x + (15 * x + 3x * x)) = 0
x(-135 + -27x + (15x + 3x2)) = 0

Combine like terms: -27x + 15x = -12x
x(-135 + -12x + 3x2) = 0
(-135 * x + -12x * x + 3x2 * x) = 0
(-135x + -12x2 + 3x3) = 0

Solving
-135x + -12x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-45 + -4x + x2) = 0

Factor a trinomial.
3x((-5 + -1x)(9 + -1x)) = 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 '(-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

Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, -5, 9}

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