10y^3=21y^2-9y

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Solution for 10y^3=21y^2-9y equation:


Simplifying
10y3 = 21y2 + -9y

Reorder the terms:
10y3 = -9y + 21y2

Solving
10y3 = -9y + 21y2

Solving for variable 'y'.

Reorder the terms:
9y + -21y2 + 10y3 = -9y + 21y2 + 9y + -21y2

Reorder the terms:
9y + -21y2 + 10y3 = -9y + 9y + 21y2 + -21y2

Combine like terms: -9y + 9y = 0
9y + -21y2 + 10y3 = 0 + 21y2 + -21y2
9y + -21y2 + 10y3 = 21y2 + -21y2

Combine like terms: 21y2 + -21y2 = 0
9y + -21y2 + 10y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(9 + -21y + 10y2) = 0

Factor a trinomial.
y((3 + -5y)(3 + -2y)) = 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 '(3 + -5y)' equal to zero and attempt to solve: Simplifying 3 + -5y = 0 Solving 3 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5y = 0 + -3 -5y = 0 + -3 Combine like terms: 0 + -3 = -3 -5y = -3 Divide each side by '-5'. y = 0.6 Simplifying y = 0.6

Subproblem 3

Set the factor '(3 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Divide each side by '-2'. y = 1.5 Simplifying y = 1.5

Solution

y = {0, 0.6, 1.5}

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