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Simplifying (4y + 6)(2 + y) = 0 Reorder the terms: (6 + 4y)(2 + y) = 0 Multiply (6 + 4y) * (2 + y) (6(2 + y) + 4y * (2 + y)) = 0 ((2 * 6 + y * 6) + 4y * (2 + y)) = 0 ((12 + 6y) + 4y * (2 + y)) = 0 (12 + 6y + (2 * 4y + y * 4y)) = 0 (12 + 6y + (8y + 4y2)) = 0 Combine like terms: 6y + 8y = 14y (12 + 14y + 4y2) = 0 Solving 12 + 14y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 7y + 2y2) = 0 Factor a trinomial. 2((2 + y)(3 + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Subproblem 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 = {-2, -1.5}
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