0=9x^3+30x^2-24x

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Solution for 0=9x^3+30x^2-24x equation: 


Simplifying
0 = 9x3 + 30x2 + -24x

Reorder the terms:
0 = -24x + 30x2 + 9x3

Solving
0 = -24x + 30x2 + 9x3

Solving for variable 'x'.
Remove the zero:
24x + -30x2 + -9x3 = -24x + 30x2 + 9x3 + 24x + -30x2 + -9x3

Reorder the terms:
24x + -30x2 + -9x3 = -24x + 24x + 30x2 + -30x2 + 9x3 + -9x3

Combine like terms: -24x + 24x = 0
24x + -30x2 + -9x3 = 0 + 30x2 + -30x2 + 9x3 + -9x3
24x + -30x2 + -9x3 = 30x2 + -30x2 + 9x3 + -9x3

Combine like terms: 30x2 + -30x2 = 0
24x + -30x2 + -9x3 = 0 + 9x3 + -9x3
24x + -30x2 + -9x3 = 9x3 + -9x3

Combine like terms: 9x3 + -9x3 = 0
24x + -30x2 + -9x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(8 + -10x + -3x2) = 0

Factor a trinomial.
3x((2 + -3x)(4 + x)) = 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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, 0.6666666667, -4}

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