2x^3-12x^2=14x

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Solution for 2x^3-12x^2=14x equation:


Simplifying
2x3 + -12x2 = 14x

Reorder the terms:
-12x2 + 2x3 = 14x

Solving
-12x2 + 2x3 = 14x

Solving for variable 'x'.

Reorder the terms:
-14x + -12x2 + 2x3 = 14x + -14x

Combine like terms: 14x + -14x = 0
-14x + -12x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-7 + -6x + x2) = 0

Factor a trinomial.
2x((-1 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {0, -1, 7}

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