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Simplifying 0 = y2 + -12y + 32 Reorder the terms: 0 = 32 + -12y + y2 Solving 0 = 32 + -12y + y2 Solving for variable 'y'. Combine like terms: 0 + -32 = -32 -32 + 12y + -1y2 = 32 + -12y + y2 + -32 + 12y + -1y2 Reorder the terms: -32 + 12y + -1y2 = 32 + -32 + -12y + 12y + y2 + -1y2 Combine like terms: 32 + -32 = 0 -32 + 12y + -1y2 = 0 + -12y + 12y + y2 + -1y2 -32 + 12y + -1y2 = -12y + 12y + y2 + -1y2 Combine like terms: -12y + 12y = 0 -32 + 12y + -1y2 = 0 + y2 + -1y2 -32 + 12y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -32 + 12y + -1y2 = 0 Factor a trinomial. (-8 + y)(4 + -1y) = 0Subproblem 1
Set the factor '(-8 + y)' equal to zero and attempt to solve: Simplifying -8 + y = 0 Solving -8 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 0 + 8 Combine like terms: -8 + 8 = 0 0 + y = 0 + 8 y = 0 + 8 Combine like terms: 0 + 8 = 8 y = 8 Simplifying y = 8Subproblem 2
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 = 4Solution
y = {8, 4}
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