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Simplifying 2y + 3 = y2 + -5 Reorder the terms: 3 + 2y = y2 + -5 Reorder the terms: 3 + 2y = -5 + y2 Solving 3 + 2y = -5 + y2 Solving for variable 'y'. Reorder the terms: 3 + 5 + 2y + -1y2 = -5 + y2 + 5 + -1y2 Combine like terms: 3 + 5 = 8 8 + 2y + -1y2 = -5 + y2 + 5 + -1y2 Reorder the terms: 8 + 2y + -1y2 = -5 + 5 + y2 + -1y2 Combine like terms: -5 + 5 = 0 8 + 2y + -1y2 = 0 + y2 + -1y2 8 + 2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 8 + 2y + -1y2 = 0 Factor a trinomial. (4 + -1y)(2 + y) = 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 '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Solution
y = {4, -2}
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