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Simplifying 2y(3y + 1)(5y + 1) = 0 Reorder the terms: 2y(1 + 3y)(5y + 1) = 0 Reorder the terms: 2y(1 + 3y)(1 + 5y) = 0 Multiply (1 + 3y) * (1 + 5y) 2y(1(1 + 5y) + 3y * (1 + 5y)) = 0 2y((1 * 1 + 5y * 1) + 3y * (1 + 5y)) = 0 2y((1 + 5y) + 3y * (1 + 5y)) = 0 2y(1 + 5y + (1 * 3y + 5y * 3y)) = 0 2y(1 + 5y + (3y + 15y2)) = 0 Combine like terms: 5y + 3y = 8y 2y(1 + 8y + 15y2) = 0 (1 * 2y + 8y * 2y + 15y2 * 2y) = 0 (2y + 16y2 + 30y3) = 0 Solving 2y + 16y2 + 30y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(1 + 8y + 15y2) = 0 Factor a trinomial. 2y((1 + 3y)(1 + 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 '(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 = -0.3333333333Subproblem 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 = -0.2Solution
y = {0, -0.3333333333, -0.2}
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