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Simplifying (4y + 6)(7 + y) = 0 Reorder the terms: (6 + 4y)(7 + y) = 0 Multiply (6 + 4y) * (7 + y) (6(7 + y) + 4y * (7 + y)) = 0 ((7 * 6 + y * 6) + 4y * (7 + y)) = 0 ((42 + 6y) + 4y * (7 + y)) = 0 (42 + 6y + (7 * 4y + y * 4y)) = 0 (42 + 6y + (28y + 4y2)) = 0 Combine like terms: 6y + 28y = 34y (42 + 34y + 4y2) = 0 Solving 42 + 34y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 17y + 2y2) = 0 Factor a trinomial. 2((7 + y)(3 + 2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 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 = {-7, -1.5}
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