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Simplifying (3y + 8)(2 + y) = 0 Reorder the terms: (8 + 3y)(2 + y) = 0 Multiply (8 + 3y) * (2 + y) (8(2 + y) + 3y * (2 + y)) = 0 ((2 * 8 + y * 8) + 3y * (2 + y)) = 0 ((16 + 8y) + 3y * (2 + y)) = 0 (16 + 8y + (2 * 3y + y * 3y)) = 0 (16 + 8y + (6y + 3y2)) = 0 Combine like terms: 8y + 6y = 14y (16 + 14y + 3y2) = 0 Solving 16 + 14y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (8 + 3y)(2 + y) = 0Subproblem 1
Set the factor '(8 + 3y)' equal to zero and attempt to solve: Simplifying 8 + 3y = 0 Solving 8 + 3y = 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 + 3y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3y = 0 + -8 3y = 0 + -8 Combine like terms: 0 + -8 = -8 3y = -8 Divide each side by '3'. y = -2.666666667 Simplifying y = -2.666666667Subproblem 2
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 = -2Solution
y = {-2.666666667, -2}
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