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Simplifying (3y + -1)(2y + 8) = 0 Reorder the terms: (-1 + 3y)(2y + 8) = 0 Reorder the terms: (-1 + 3y)(8 + 2y) = 0 Multiply (-1 + 3y) * (8 + 2y) (-1(8 + 2y) + 3y * (8 + 2y)) = 0 ((8 * -1 + 2y * -1) + 3y * (8 + 2y)) = 0 ((-8 + -2y) + 3y * (8 + 2y)) = 0 (-8 + -2y + (8 * 3y + 2y * 3y)) = 0 (-8 + -2y + (24y + 6y2)) = 0 Combine like terms: -2y + 24y = 22y (-8 + 22y + 6y2) = 0 Solving -8 + 22y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 11y + 3y2) = 0 Factor a trinomial. 2((-4 + -1y)(1 + -3y)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Solution
y = {-4, 0.3333333333}
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