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Simplifying -5y(y + 6)(y + 2) = 0 Reorder the terms: -5y(6 + y)(y + 2) = 0 Reorder the terms: -5y(6 + y)(2 + y) = 0 Multiply (6 + y) * (2 + y) -5y(6(2 + y) + y(2 + y)) = 0 -5y((2 * 6 + y * 6) + y(2 + y)) = 0 -5y((12 + 6y) + y(2 + y)) = 0 -5y(12 + 6y + (2 * y + y * y)) = 0 -5y(12 + 6y + (2y + y2)) = 0 Combine like terms: 6y + 2y = 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((6 + y)(2 + y)) = 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 '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 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 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Subproblem 3
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Solution
y = {0, -6, -2}
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