3y^3+36y=24y^2

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Solution for 3y^3+36y=24y^2 equation:


Simplifying
3y3 + 36y = 24y2

Reorder the terms:
36y + 3y3 = 24y2

Solving
36y + 3y3 = 24y2

Solving for variable 'y'.

Reorder the terms:
36y + -24y2 + 3y3 = 24y2 + -24y2

Combine like terms: 24y2 + -24y2 = 0
36y + -24y2 + 3y3 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(12 + -8y + y2) = 0

Factor a trinomial.
3y((2 + -1y)(6 + -1y)) = 0

Ignore the factor 3.

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 '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Subproblem 3

Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6

Solution

y = {0, 2, 6}

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