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Simplifying (8 + y)(4y + 6) = 0 Reorder the terms: (8 + y)(6 + 4y) = 0 Multiply (8 + y) * (6 + 4y) (8(6 + 4y) + y(6 + 4y)) = 0 ((6 * 8 + 4y * 8) + y(6 + 4y)) = 0 ((48 + 32y) + y(6 + 4y)) = 0 (48 + 32y + (6 * y + 4y * y)) = 0 (48 + 32y + (6y + 4y2)) = 0 Combine like terms: 32y + 6y = 38y (48 + 38y + 4y2) = 0 Solving 48 + 38y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 19y + 2y2) = 0 Factor a trinomial. 2((8 + y)(3 + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve: Simplifying 8 + y = 0 Solving 8 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + y = 0 + -8 y = 0 + -8 Combine like terms: 0 + -8 = -8 y = -8 Simplifying y = -8Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5Solution
y = {-8, -1.5}
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