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Simplifying 3Y2 + 2Y + -12 = Y2 Reorder the terms: -12 + 2Y + 3Y2 = Y2 Solving -12 + 2Y + 3Y2 = Y2 Solving for variable 'Y'. Combine like terms: 3Y2 + -1Y2 = 2Y2 -12 + 2Y + 2Y2 = Y2 + -1Y2 Combine like terms: Y2 + -1Y2 = 0 -12 + 2Y + 2Y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + Y + Y2) = 0 Factor a trinomial. 2((-3 + -1Y)(2 + -1Y)) = 0 Ignore the factor 2.Subproblem 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 '(2 + -1Y)' equal to zero and attempt to solve: Simplifying 2 + -1Y = 0 Solving 2 + -1Y = 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 + -1Y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1Y = 0 + -2 -1Y = 0 + -2 Combine like terms: 0 + -2 = -2 -1Y = -2 Divide each side by '-1'. Y = 2 Simplifying Y = 2Solution
Y = {-3, 2}
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