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Simplifying (2y + 1)(y + 3) = 12 Reorder the terms: (1 + 2y)(y + 3) = 12 Reorder the terms: (1 + 2y)(3 + y) = 12 Multiply (1 + 2y) * (3 + y) (1(3 + y) + 2y * (3 + y)) = 12 ((3 * 1 + y * 1) + 2y * (3 + y)) = 12 ((3 + 1y) + 2y * (3 + y)) = 12 (3 + 1y + (3 * 2y + y * 2y)) = 12 (3 + 1y + (6y + 2y2)) = 12 Combine like terms: 1y + 6y = 7y (3 + 7y + 2y2) = 12 Solving 3 + 7y + 2y2 = 12 Solving for variable 'y'. Reorder the terms: 3 + -12 + 7y + 2y2 = 12 + -12 Combine like terms: 3 + -12 = -9 -9 + 7y + 2y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -9 + 7y + 2y2 = 0 Factor a trinomial. (-9 + -2y)(1 + -1y) = 0Subproblem 1
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 = -4.5Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {-4.5, 1}
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