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Simplifying -4y(y + 6)(y + 7) = 0 Reorder the terms: -4y(6 + y)(y + 7) = 0 Reorder the terms: -4y(6 + y)(7 + y) = 0 Multiply (6 + y) * (7 + y) -4y(6(7 + y) + y(7 + y)) = 0 -4y((7 * 6 + y * 6) + y(7 + y)) = 0 -4y((42 + 6y) + y(7 + y)) = 0 -4y(42 + 6y + (7 * y + y * y)) = 0 -4y(42 + 6y + (7y + y2)) = 0 Combine like terms: 6y + 7y = 13y -4y(42 + 13y + y2) = 0 (42 * -4y + 13y * -4y + y2 * -4y) = 0 (-168y + -52y2 + -4y3) = 0 Solving -168y + -52y2 + -4y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-4y'. -4y(42 + 13y + y2) = 0 Factor a trinomial. -4y((7 + y)(6 + y)) = 0 Ignore the factor -4.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 '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 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, -7, -6}
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