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Simplifying (2y + 4)(6y + -24) = 0 Reorder the terms: (4 + 2y)(6y + -24) = 0 Reorder the terms: (4 + 2y)(-24 + 6y) = 0 Multiply (4 + 2y) * (-24 + 6y) (4(-24 + 6y) + 2y * (-24 + 6y)) = 0 ((-24 * 4 + 6y * 4) + 2y * (-24 + 6y)) = 0 ((-96 + 24y) + 2y * (-24 + 6y)) = 0 (-96 + 24y + (-24 * 2y + 6y * 2y)) = 0 (-96 + 24y + (-48y + 12y2)) = 0 Combine like terms: 24y + -48y = -24y (-96 + -24y + 12y2) = 0 Solving -96 + -24y + 12y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '12'. 12(-8 + -2y + y2) = 0 Factor a trinomial. 12((-2 + -1y)(4 + -1y)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 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 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 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 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Solution
y = {-2, 4}
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