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Simplifying -3y(y + 6)(4y + -5) = 0 Reorder the terms: -3y(6 + y)(4y + -5) = 0 Reorder the terms: -3y(6 + y)(-5 + 4y) = 0 Multiply (6 + y) * (-5 + 4y) -3y(6(-5 + 4y) + y(-5 + 4y)) = 0 -3y((-5 * 6 + 4y * 6) + y(-5 + 4y)) = 0 -3y((-30 + 24y) + y(-5 + 4y)) = 0 -3y(-30 + 24y + (-5 * y + 4y * y)) = 0 -3y(-30 + 24y + (-5y + 4y2)) = 0 Combine like terms: 24y + -5y = 19y -3y(-30 + 19y + 4y2) = 0 (-30 * -3y + 19y * -3y + 4y2 * -3y) = 0 (90y + -57y2 + -12y3) = 0 Solving 90y + -57y2 + -12y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(30 + -19y + -4y2) = 0 Factor a trinomial. 3y((5 + -4y)(6 + y)) = 0 Ignore the factor 3.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 '(5 + -4y)' equal to zero and attempt to solve: Simplifying 5 + -4y = 0 Solving 5 + -4y = 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 + -4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4y = 0 + -5 -4y = 0 + -5 Combine like terms: 0 + -5 = -5 -4y = -5 Divide each side by '-4'. y = 1.25 Simplifying y = 1.25Subproblem 3
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 = -6Solution
y = {0, 1.25, -6}
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