5x^3-14x^2=3x

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Solution for 5x^3-14x^2=3x equation:


Simplifying
5x3 + -14x2 = 3x

Reorder the terms:
-14x2 + 5x3 = 3x

Solving
-14x2 + 5x3 = 3x

Solving for variable 'x'.

Reorder the terms:
-3x + -14x2 + 5x3 = 3x + -3x

Combine like terms: 3x + -3x = 0
-3x + -14x2 + 5x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -14x + 5x2) = 0

Factor a trinomial.
x((-1 + -5x)(3 + -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 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2

Subproblem 3

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, -0.2, 3}

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