3x^3=x^2+4x

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


Simplifying
3x3 = x2 + 4x

Reorder the terms:
3x3 = 4x + x2

Solving
3x3 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
-4x + -1x2 + 3x3 = 4x + x2 + -4x + -1x2

Reorder the terms:
-4x + -1x2 + 3x3 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-4x + -1x2 + 3x3 = 0 + x2 + -1x2
-4x + -1x2 + 3x3 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4x + -1x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + -1x + 3x2) = 0

Factor a trinomial.
x((-1 + -1x)(4 + -3x)) = 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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 3

Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {0, -1, 1.333333333}

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