-12x^3-21x^2=-6x

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Solution for -12x^3-21x^2=-6x equation:


Simplifying
-12x3 + -21x2 = -6x

Reorder the terms:
-21x2 + -12x3 = -6x

Solving
-21x2 + -12x3 = -6x

Solving for variable 'x'.

Reorder the terms:
6x + -21x2 + -12x3 = -6x + 6x

Combine like terms: -6x + 6x = 0
6x + -21x2 + -12x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(2 + -7x + -4x2) = 0

Factor a trinomial.
3x((1 + -4x)(2 + x)) = 0

Ignore the factor 3.

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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Subproblem 3

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

Solution

x = {0, 0.25, -2}

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