(2(y^3))-(9(y^2))-(5y)=0

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Solution for (2(y^3))-(9(y^2))-(5y)=0 equation:


Simplifying
(2(y3)) + -1(9(y2)) + -1(5y) = 0

Remove parenthesis around (9y2)
(2y3) + -1 * 9y2 + -1(5y) = 0

Multiply -1 * 9
(2y3) + -9y2 + -1(5y) = 0

Remove parenthesis around (5y)
(2y3) + -9y2 + -1 * 5y = 0

Multiply -1 * 5
(2y3) + -9y2 + -5y = 0

Reorder the terms:
-5y + -9y2 + (2y3) = 0

Solving
-5y + -9y2 + (2y3) = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-5 + -9y + (2y2)) = 0

Factor a trinomial.
y((-1 + -2y)(5 + -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 '(-1 + -2y)' equal to zero and attempt to solve: Simplifying -1 + -2y = 0 Solving -1 + -2y = 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 + -2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2y = 0 + 1 -2y = 0 + 1 Combine like terms: 0 + 1 = 1 -2y = 1 Divide each side by '-2'. y = -0.5 Simplifying y = -0.5

Subproblem 3

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

Solution

y = {0, -0.5, 5}

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