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Simplifying 2y2 + -12 + -4y = y2 + -3y Reorder the terms: -12 + -4y + 2y2 = y2 + -3y Reorder the terms: -12 + -4y + 2y2 = -3y + y2 Solving -12 + -4y + 2y2 = -3y + y2 Solving for variable 'y'. Reorder the terms: -12 + -4y + 3y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2 Combine like terms: -4y + 3y = -1y -12 + -1y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -12 + -1y + 1y2 = -3y + y2 + 3y + -1y2 Reorder the terms: -12 + -1y + 1y2 = -3y + 3y + y2 + -1y2 Combine like terms: -3y + 3y = 0 -12 + -1y + 1y2 = 0 + y2 + -1y2 -12 + -1y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + -1y + 1y2 = 0 Factor a trinomial. (-3 + -1y)(4 + -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 '(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 = {-3, 4}
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