40y=13y^2-y^3

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Solution for 40y=13y^2-y^3 equation:


Simplifying
40y = 13y2 + -1y3

Solving
40y = 13y2 + -1y3

Solving for variable 'y'.

Reorder the terms:
40y + -13y2 + y3 = 13y2 + -13y2 + -1y3 + y3

Combine like terms: 13y2 + -13y2 = 0
40y + -13y2 + y3 = 0 + -1y3 + y3
40y + -13y2 + y3 = -1y3 + y3

Combine like terms: -1y3 + y3 = 0
40y + -13y2 + y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(40 + -13y + y2) = 0

Factor a trinomial.
y((5 + -1y)(8 + -1y)) = 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 '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5

Subproblem 3

Set the factor '(8 + -1y)' equal to zero and attempt to solve: Simplifying 8 + -1y = 0 Solving 8 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1y = 0 + -8 -1y = 0 + -8 Combine like terms: 0 + -8 = -8 -1y = -8 Divide each side by '-1'. y = 8 Simplifying y = 8

Solution

y = {0, 5, 8}

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