120x^3-60x^2-180x=0

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Solution for 120x^3-60x^2-180x=0 equation:


Simplifying
120x3 + -60x2 + -180x = 0

Reorder the terms:
-180x + -60x2 + 120x3 = 0

Solving
-180x + -60x2 + 120x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '60x'.
60x(-3 + -1x + 2x2) = 0

Factor a trinomial.
60x((-1 + -1x)(3 + -2x)) = 0

Ignore the factor 60.

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 '(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

Solution

x = {0, -1, 1.5}

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