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Simplifying 23 + -3y = y2 + -5 Reorder the terms: 23 + -3y = -5 + y2 Solving 23 + -3y = -5 + y2 Solving for variable 'y'. Reorder the terms: 23 + 5 + -3y + -1y2 = -5 + y2 + 5 + -1y2 Combine like terms: 23 + 5 = 28 28 + -3y + -1y2 = -5 + y2 + 5 + -1y2 Reorder the terms: 28 + -3y + -1y2 = -5 + 5 + y2 + -1y2 Combine like terms: -5 + 5 = 0 28 + -3y + -1y2 = 0 + y2 + -1y2 28 + -3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 28 + -3y + -1y2 = 0 Factor a trinomial. (4 + -1y)(7 + 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 '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Solution
y = {4, -7}
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