4y^3+3y^2-y=0

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Solution for 4y^3+3y^2-y=0 equation:


Simplifying
4y3 + 3y2 + -1y = 0

Reorder the terms:
-1y + 3y2 + 4y3 = 0

Solving
-1y + 3y2 + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 3y + 4y2) = 0

Factor a trinomial.
y((-1 + -1y)(1 + -4y)) = 0

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

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

Subproblem 3

Set the factor '(1 + -4y)' equal to zero and attempt to solve: Simplifying 1 + -4y = 0 Solving 1 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4y = 0 + -1 -4y = 0 + -1 Combine like terms: 0 + -1 = -1 -4y = -1 Divide each side by '-4'. y = 0.25 Simplifying y = 0.25

Solution

y = {0, -1, 0.25}

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