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Simplifying 3Y(2Y + -7) = 45 Reorder the terms: 3Y(-7 + 2Y) = 45 (-7 * 3Y + 2Y * 3Y) = 45 (-21Y + 6Y2) = 45 Solving -21Y + 6Y2 = 45 Solving for variable 'Y'. Reorder the terms: -45 + -21Y + 6Y2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -21Y + 6Y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -7Y + 2Y2) = 0 Factor a trinomial. 3((-3 + -2Y)(5 + -1Y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2Y)' equal to zero and attempt to solve: Simplifying -3 + -2Y = 0 Solving -3 + -2Y = 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 + -2Y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2Y = 0 + 3 -2Y = 0 + 3 Combine like terms: 0 + 3 = 3 -2Y = 3 Divide each side by '-2'. Y = -1.5 Simplifying Y = -1.5Subproblem 2
Set the factor '(5 + -1Y)' equal to zero and attempt to solve: Simplifying 5 + -1Y = 0 Solving 5 + -1Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1Y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1Y = 0 + -5 -1Y = 0 + -5 Combine like terms: 0 + -5 = -5 -1Y = -5 Divide each side by '-1'. Y = 5 Simplifying Y = 5Solution
Y = {-1.5, 5}
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