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Simplifying -2y(y + 5)(y + 6) = 0 Reorder the terms: -2y(5 + y)(y + 6) = 0 Reorder the terms: -2y(5 + y)(6 + y) = 0 Multiply (5 + y) * (6 + y) -2y(5(6 + y) + y(6 + y)) = 0 -2y((6 * 5 + y * 5) + y(6 + y)) = 0 -2y((30 + 5y) + y(6 + y)) = 0 -2y(30 + 5y + (6 * y + y * y)) = 0 -2y(30 + 5y + (6y + y2)) = 0 Combine like terms: 5y + 6y = 11y -2y(30 + 11y + y2) = 0 (30 * -2y + 11y * -2y + y2 * -2y) = 0 (-60y + -22y2 + -2y3) = 0 Solving -60y + -22y2 + -2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-2y'. -2y(30 + 11y + y2) = 0 Factor a trinomial. -2y((6 + y)(5 + y)) = 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 + 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 '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Solution
y = {0, -6, -5}
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