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Simplifying (3Y + 1)(2Y + -3) = -8Y + -1 Reorder the terms: (1 + 3Y)(2Y + -3) = -8Y + -1 Reorder the terms: (1 + 3Y)(-3 + 2Y) = -8Y + -1 Multiply (1 + 3Y) * (-3 + 2Y) (1(-3 + 2Y) + 3Y * (-3 + 2Y)) = -8Y + -1 ((-3 * 1 + 2Y * 1) + 3Y * (-3 + 2Y)) = -8Y + -1 ((-3 + 2Y) + 3Y * (-3 + 2Y)) = -8Y + -1 (-3 + 2Y + (-3 * 3Y + 2Y * 3Y)) = -8Y + -1 (-3 + 2Y + (-9Y + 6Y2)) = -8Y + -1 Combine like terms: 2Y + -9Y = -7Y (-3 + -7Y + 6Y2) = -8Y + -1 Reorder the terms: -3 + -7Y + 6Y2 = -1 + -8Y Solving -3 + -7Y + 6Y2 = -1 + -8Y Solving for variable 'Y'. Reorder the terms: -3 + 1 + -7Y + 8Y + 6Y2 = -1 + -8Y + 1 + 8Y Combine like terms: -3 + 1 = -2 -2 + -7Y + 8Y + 6Y2 = -1 + -8Y + 1 + 8Y Combine like terms: -7Y + 8Y = 1Y -2 + 1Y + 6Y2 = -1 + -8Y + 1 + 8Y Reorder the terms: -2 + 1Y + 6Y2 = -1 + 1 + -8Y + 8Y Combine like terms: -1 + 1 = 0 -2 + 1Y + 6Y2 = 0 + -8Y + 8Y -2 + 1Y + 6Y2 = -8Y + 8Y Combine like terms: -8Y + 8Y = 0 -2 + 1Y + 6Y2 = 0 Factor a trinomial. (-2 + -3Y)(1 + -2Y) = 0Subproblem 1
Set the factor '(-2 + -3Y)' equal to zero and attempt to solve: Simplifying -2 + -3Y = 0 Solving -2 + -3Y = 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 + -3Y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3Y = 0 + 2 -3Y = 0 + 2 Combine like terms: 0 + 2 = 2 -3Y = 2 Divide each side by '-3'. Y = -0.6666666667 Simplifying Y = -0.6666666667Subproblem 2
Set the factor '(1 + -2Y)' equal to zero and attempt to solve: Simplifying 1 + -2Y = 0 Solving 1 + -2Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2Y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2Y = 0 + -1 -2Y = 0 + -1 Combine like terms: 0 + -1 = -1 -2Y = -1 Divide each side by '-2'. Y = 0.5 Simplifying Y = 0.5Solution
Y = {-0.6666666667, 0.5}
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