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Simplifying (Y + 3)(2Y + -7) = 0 Reorder the terms: (3 + Y)(2Y + -7) = 0 Reorder the terms: (3 + Y)(-7 + 2Y) = 0 Multiply (3 + Y) * (-7 + 2Y) (3(-7 + 2Y) + Y(-7 + 2Y)) = 0 ((-7 * 3 + 2Y * 3) + Y(-7 + 2Y)) = 0 ((-21 + 6Y) + Y(-7 + 2Y)) = 0 (-21 + 6Y + (-7 * Y + 2Y * Y)) = 0 (-21 + 6Y + (-7Y + 2Y2)) = 0 Combine like terms: 6Y + -7Y = -1Y (-21 + -1Y + 2Y2) = 0 Solving -21 + -1Y + 2Y2 = 0 Solving for variable 'Y'. Factor a trinomial. (-3 + -1Y)(7 + -2Y) = 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 '(7 + -2Y)' equal to zero and attempt to solve: Simplifying 7 + -2Y = 0 Solving 7 + -2Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2Y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2Y = 0 + -7 -2Y = 0 + -7 Combine like terms: 0 + -7 = -7 -2Y = -7 Divide each side by '-2'. Y = 3.5 Simplifying Y = 3.5Solution
Y = {-3, 3.5}
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