3x^3=15x+4x^2

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Solution for 3x^3=15x+4x^2 equation: 


Simplifying
3x3 = 15x + 4x2

Solving
3x3 = 15x + 4x2

Solving for variable 'x'.

Reorder the terms:
-15x + -4x2 + 3x3 = 15x + 4x2 + -15x + -4x2

Reorder the terms:
-15x + -4x2 + 3x3 = 15x + -15x + 4x2 + -4x2

Combine like terms: 15x + -15x = 0
-15x + -4x2 + 3x3 = 0 + 4x2 + -4x2
-15x + -4x2 + 3x3 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-15x + -4x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + -4x + 3x2) = 0

Factor a trinomial.
x((-5 + -3x)(3 + -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 '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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, -1.666666667, 3}

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