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Simplifying (y + 3)(2y + -1) = 9 Reorder the terms: (3 + y)(2y + -1) = 9 Reorder the terms: (3 + y)(-1 + 2y) = 9 Multiply (3 + y) * (-1 + 2y) (3(-1 + 2y) + y(-1 + 2y)) = 9 ((-1 * 3 + 2y * 3) + y(-1 + 2y)) = 9 ((-3 + 6y) + y(-1 + 2y)) = 9 (-3 + 6y + (-1 * y + 2y * y)) = 9 (-3 + 6y + (-1y + 2y2)) = 9 Combine like terms: 6y + -1y = 5y (-3 + 5y + 2y2) = 9 Solving -3 + 5y + 2y2 = 9 Solving for variable 'y'. Reorder the terms: -3 + -9 + 5y + 2y2 = 9 + -9 Combine like terms: -3 + -9 = -12 -12 + 5y + 2y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -12 + 5y + 2y2 = 0 Factor a trinomial. (-4 + -1y)(3 + -2y) = 0Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4Subproblem 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 = {-4, 1.5}
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