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Simplifying 5y(y + -2)(y + -6) = 0 Reorder the terms: 5y(-2 + y)(y + -6) = 0 Reorder the terms: 5y(-2 + y)(-6 + y) = 0 Multiply (-2 + y) * (-6 + y) 5y(-2(-6 + y) + y(-6 + y)) = 0 5y((-6 * -2 + y * -2) + y(-6 + y)) = 0 5y((12 + -2y) + y(-6 + y)) = 0 5y(12 + -2y + (-6 * y + y * y)) = 0 5y(12 + -2y + (-6y + y2)) = 0 Combine like terms: -2y + -6y = -8y 5y(12 + -8y + y2) = 0 (12 * 5y + -8y * 5y + y2 * 5y) = 0 (60y + -40y2 + 5y3) = 0 Solving 60y + -40y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(12 + -8y + y2) = 0 Factor a trinomial. 5y((2 + -1y)(6 + -1y)) = 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 '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Subproblem 3
Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 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 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6Solution
y = {0, 2, 6}
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