3x^3-16x^2=-5x

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Solution for 3x^3-16x^2=-5x equation:


Simplifying
3x3 + -16x2 = -5x

Reorder the terms:
-16x2 + 3x3 = -5x

Solving
-16x2 + 3x3 = -5x

Solving for variable 'x'.

Reorder the terms:
5x + -16x2 + 3x3 = -5x + 5x

Combine like terms: -5x + 5x = 0
5x + -16x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -16x + 3x2) = 0

Factor a trinomial.
x((1 + -3x)(5 + -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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Subproblem 3

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {0, 0.3333333333, 5}

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