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Simplifying (3 + Y)(3Y + -5) = 0 Reorder the terms: (3 + Y)(-5 + 3Y) = 0 Multiply (3 + Y) * (-5 + 3Y) (3(-5 + 3Y) + Y(-5 + 3Y)) = 0 ((-5 * 3 + 3Y * 3) + Y(-5 + 3Y)) = 0 ((-15 + 9Y) + Y(-5 + 3Y)) = 0 (-15 + 9Y + (-5 * Y + 3Y * Y)) = 0 (-15 + 9Y + (-5Y + 3Y2)) = 0 Combine like terms: 9Y + -5Y = 4Y (-15 + 4Y + 3Y2) = 0 Solving -15 + 4Y + 3Y2 = 0 Solving for variable 'Y'. Factor a trinomial. (-3 + -1Y)(5 + -3Y) = 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 '(5 + -3Y)' equal to zero and attempt to solve: Simplifying 5 + -3Y = 0 Solving 5 + -3Y = 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 + -3Y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3Y = 0 + -5 -3Y = 0 + -5 Combine like terms: 0 + -5 = -5 -3Y = -5 Divide each side by '-3'. Y = 1.666666667 Simplifying Y = 1.666666667Solution
Y = {-3, 1.666666667}
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