2x^3=x(3x+20)

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Solution for 2x^3=x(3x+20) equation: 


Simplifying
2x3 = x(3x + 20)

Reorder the terms:
2x3 = x(20 + 3x)
2x3 = (20 * x + 3x * x)
2x3 = (20x + 3x2)

Solving
2x3 = 20x + 3x2

Solving for variable 'x'.

Reorder the terms:
-20x + -3x2 + 2x3 = 20x + 3x2 + -20x + -3x2

Reorder the terms:
-20x + -3x2 + 2x3 = 20x + -20x + 3x2 + -3x2

Combine like terms: 20x + -20x = 0
-20x + -3x2 + 2x3 = 0 + 3x2 + -3x2
-20x + -3x2 + 2x3 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-20x + -3x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20 + -3x + 2x2) = 0

Factor a trinomial.
x((-5 + -2x)(4 + -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 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -2.5, 4}

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