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Simplifying 2y2 + 24y + 12 = y2 + 32y + -3 Reorder the terms: 12 + 24y + 2y2 = y2 + 32y + -3 Reorder the terms: 12 + 24y + 2y2 = -3 + 32y + y2 Solving 12 + 24y + 2y2 = -3 + 32y + y2 Solving for variable 'y'. Reorder the terms: 12 + 3 + 24y + -32y + 2y2 + -1y2 = -3 + 32y + y2 + 3 + -32y + -1y2 Combine like terms: 12 + 3 = 15 15 + 24y + -32y + 2y2 + -1y2 = -3 + 32y + y2 + 3 + -32y + -1y2 Combine like terms: 24y + -32y = -8y 15 + -8y + 2y2 + -1y2 = -3 + 32y + y2 + 3 + -32y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 15 + -8y + 1y2 = -3 + 32y + y2 + 3 + -32y + -1y2 Reorder the terms: 15 + -8y + 1y2 = -3 + 3 + 32y + -32y + y2 + -1y2 Combine like terms: -3 + 3 = 0 15 + -8y + 1y2 = 0 + 32y + -32y + y2 + -1y2 15 + -8y + 1y2 = 32y + -32y + y2 + -1y2 Combine like terms: 32y + -32y = 0 15 + -8y + 1y2 = 0 + y2 + -1y2 15 + -8y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 15 + -8y + 1y2 = 0 Factor a trinomial. (3 + -1y)(5 + -1y) = 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 '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Solution
y = {3, 5}
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