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Simplifying 2y(3y + 1)(5y + 3) = 0 Reorder the terms: 2y(1 + 3y)(5y + 3) = 0 Reorder the terms: 2y(1 + 3y)(3 + 5y) = 0 Multiply (1 + 3y) * (3 + 5y) 2y(1(3 + 5y) + 3y * (3 + 5y)) = 0 2y((3 * 1 + 5y * 1) + 3y * (3 + 5y)) = 0 2y((3 + 5y) + 3y * (3 + 5y)) = 0 2y(3 + 5y + (3 * 3y + 5y * 3y)) = 0 2y(3 + 5y + (9y + 15y2)) = 0 Combine like terms: 5y + 9y = 14y 2y(3 + 14y + 15y2) = 0 (3 * 2y + 14y * 2y + 15y2 * 2y) = 0 (6y + 28y2 + 30y3) = 0 Solving 6y + 28y2 + 30y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(3 + 14y + 15y2) = 0 Factor a trinomial. 2y((3 + 5y)(1 + 3y)) = 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 + 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 = -0.6Subproblem 3
Set the factor '(1 + 3y)' equal to zero and attempt to solve: Simplifying 1 + 3y = 0 Solving 1 + 3y = 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 + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3y = 0 + -1 3y = 0 + -1 Combine like terms: 0 + -1 = -1 3y = -1 Divide each side by '3'. y = -0.3333333333 Simplifying y = -0.3333333333Solution
y = {0, -0.6, -0.3333333333}
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