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Simplifying 5y(2y + 1)(2y + 3) = 0 Reorder the terms: 5y(1 + 2y)(2y + 3) = 0 Reorder the terms: 5y(1 + 2y)(3 + 2y) = 0 Multiply (1 + 2y) * (3 + 2y) 5y(1(3 + 2y) + 2y * (3 + 2y)) = 0 5y((3 * 1 + 2y * 1) + 2y * (3 + 2y)) = 0 5y((3 + 2y) + 2y * (3 + 2y)) = 0 5y(3 + 2y + (3 * 2y + 2y * 2y)) = 0 5y(3 + 2y + (6y + 4y2)) = 0 Combine like terms: 2y + 6y = 8y 5y(3 + 8y + 4y2) = 0 (3 * 5y + 8y * 5y + 4y2 * 5y) = 0 (15y + 40y2 + 20y3) = 0 Solving 15y + 40y2 + 20y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(3 + 8y + 4y2) = 0 Factor a trinomial. 5y((3 + 2y)(1 + 2y)) = 0 Ignore the factor 5.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 '(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, -1.5, -0.5}
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