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Simplifying (4 + y)(4y + 2) = 0 Reorder the terms: (4 + y)(2 + 4y) = 0 Multiply (4 + y) * (2 + 4y) (4(2 + 4y) + y(2 + 4y)) = 0 ((2 * 4 + 4y * 4) + y(2 + 4y)) = 0 ((8 + 16y) + y(2 + 4y)) = 0 (8 + 16y + (2 * y + 4y * y)) = 0 (8 + 16y + (2y + 4y2)) = 0 Combine like terms: 16y + 2y = 18y (8 + 18y + 4y2) = 0 Solving 8 + 18y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9y + 2y2) = 0 Factor a trinomial. 2((4 + y)(1 + 2y)) = 0 Ignore the factor 2.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 '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 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 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5Solution
y = {-4, -0.5}
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