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Simplifying (3 + y)(2y + -9) = 0 Reorder the terms: (3 + y)(-9 + 2y) = 0 Multiply (3 + y) * (-9 + 2y) (3(-9 + 2y) + y(-9 + 2y)) = 0 ((-9 * 3 + 2y * 3) + y(-9 + 2y)) = 0 ((-27 + 6y) + y(-9 + 2y)) = 0 (-27 + 6y + (-9 * y + 2y * y)) = 0 (-27 + 6y + (-9y + 2y2)) = 0 Combine like terms: 6y + -9y = -3y (-27 + -3y + 2y2) = 0 Solving -27 + -3y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (-3 + -1y)(9 + -2y) = 0Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 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 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3Subproblem 2
Set the factor '(9 + -2y)' equal to zero and attempt to solve: Simplifying 9 + -2y = 0 Solving 9 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2y = 0 + -9 -2y = 0 + -9 Combine like terms: 0 + -9 = -9 -2y = -9 Divide each side by '-2'. y = 4.5 Simplifying y = 4.5Solution
y = {-3, 4.5}
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