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Simplifying 2y(5y + 6)(2y + 3) = 0 Reorder the terms: 2y(6 + 5y)(2y + 3) = 0 Reorder the terms: 2y(6 + 5y)(3 + 2y) = 0 Multiply (6 + 5y) * (3 + 2y) 2y(6(3 + 2y) + 5y * (3 + 2y)) = 0 2y((3 * 6 + 2y * 6) + 5y * (3 + 2y)) = 0 2y((18 + 12y) + 5y * (3 + 2y)) = 0 2y(18 + 12y + (3 * 5y + 2y * 5y)) = 0 2y(18 + 12y + (15y + 10y2)) = 0 Combine like terms: 12y + 15y = 27y 2y(18 + 27y + 10y2) = 0 (18 * 2y + 27y * 2y + 10y2 * 2y) = 0 (36y + 54y2 + 20y3) = 0 Solving 36y + 54y2 + 20y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(18 + 27y + 10y2) = 0 Factor a trinomial. 2y((3 + 2y)(6 + 5y)) = 0 Ignore the factor 2.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 = 0Subproblem 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 = -1.5Subproblem 3
Set the factor '(6 + 5y)' equal to zero and attempt to solve: Simplifying 6 + 5y = 0 Solving 6 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5y = 0 + -6 5y = 0 + -6 Combine like terms: 0 + -6 = -6 5y = -6 Divide each side by '5'. y = -1.2 Simplifying y = -1.2Solution
y = {0, -1.5, -1.2}
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