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Simplifying 5(y + 3)(-1y + -4) = 0 Reorder the terms: 5(3 + y)(-1y + -4) = 0 Reorder the terms: 5(3 + y)(-4 + -1y) = 0 Multiply (3 + y) * (-4 + -1y) 5(3(-4 + -1y) + y(-4 + -1y)) = 0 5((-4 * 3 + -1y * 3) + y(-4 + -1y)) = 0 5((-12 + -3y) + y(-4 + -1y)) = 0 5(-12 + -3y + (-4 * y + -1y * y)) = 0 5(-12 + -3y + (-4y + -1y2)) = 0 Combine like terms: -3y + -4y = -7y 5(-12 + -7y + -1y2) = 0 (-12 * 5 + -7y * 5 + -1y2 * 5) = 0 (-60 + -35y + -5y2) = 0 Solving -60 + -35y + -5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-5'. -5(12 + 7y + y2) = 0 Factor a trinomial. -5((4 + y)(3 + y)) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3Solution
y = {-4, -3}
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