2x^3-x^2=6x

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Solution for 2x^3-x^2=6x equation:


Simplifying
2x3 + -1x2 = 6x

Reorder the terms:
-1x2 + 2x3 = 6x

Solving
-1x2 + 2x3 = 6x

Solving for variable 'x'.

Reorder the terms:
-6x + -1x2 + 2x3 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6x + -1x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -1x + 2x2) = 0

Factor a trinomial.
x((-3 + -2x)(2 + -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 '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0, -1.5, 2}

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