10y^3+17y^2+3y=0

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Solution for 10y^3+17y^2+3y=0 equation:


Simplifying
10y3 + 17y2 + 3y = 0

Reorder the terms:
3y + 17y2 + 10y3 = 0

Solving
3y + 17y2 + 10y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + 17y + 10y2) = 0

Factor a trinomial.
y((3 + 2y)(1 + 5y)) = 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 + 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

Subproblem 3

Set the factor '(1 + 5y)' equal to zero and attempt to solve: Simplifying 1 + 5y = 0 Solving 1 + 5y = 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 + 5y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5y = 0 + -1 5y = 0 + -1 Combine like terms: 0 + -1 = -1 5y = -1 Divide each side by '5'. y = -0.2 Simplifying y = -0.2

Solution

y = {0, -1.5, -0.2}

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