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Simplifying (4y3 + 12y2 + 5y) = 0 Reorder the terms: (5y + 12y2 + 4y3) = 0 Remove parenthesis around (5y + 12y2 + 4y3) 5y + 12y2 + 4y3 = 0 Solving 5y + 12y2 + 4y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(5 + 12y + 4y2) = 0 Factor a trinomial. y((5 + 2y)(1 + 2y)) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 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 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5Subproblem 3
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 = -0.5Solution
y = {0, -2.5, -0.5}
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