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Simplifying (3 + y)(3y + 8) = 0 Reorder the terms: (3 + y)(8 + 3y) = 0 Multiply (3 + y) * (8 + 3y) (3(8 + 3y) + y(8 + 3y)) = 0 ((8 * 3 + 3y * 3) + y(8 + 3y)) = 0 ((24 + 9y) + y(8 + 3y)) = 0 (24 + 9y + (8 * y + 3y * y)) = 0 (24 + 9y + (8y + 3y2)) = 0 Combine like terms: 9y + 8y = 17y (24 + 17y + 3y2) = 0 Solving 24 + 17y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (3 + y)(8 + 3y) = 0Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 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 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3Subproblem 2
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 = -2.666666667Solution
y = {-3, -2.666666667}
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