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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 = -3y 2y(-18 + -3y + 10y2) = 0 (-18 * 2y + -3y * 2y + 10y2 * 2y) = 0 (-36y + -6y2 + 20y3) = 0 Solving -36y + -6y2 + 20y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-18 + -3y + 10y2) = 0 Factor a trinomial. 2y((-6 + -5y)(3 + -2y)) = 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 '(-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 = -1.2Subproblem 3
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 = 1.5Solution
y = {0, -1.2, 1.5}
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