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Simplifying (4Y + 6)(3 + -1Y) = 0 Reorder the terms: (6 + 4Y)(3 + -1Y) = 0 Multiply (6 + 4Y) * (3 + -1Y) (6(3 + -1Y) + 4Y * (3 + -1Y)) = 0 ((3 * 6 + -1Y * 6) + 4Y * (3 + -1Y)) = 0 ((18 + -6Y) + 4Y * (3 + -1Y)) = 0 (18 + -6Y + (3 * 4Y + -1Y * 4Y)) = 0 (18 + -6Y + (12Y + -4Y2)) = 0 Combine like terms: -6Y + 12Y = 6Y (18 + 6Y + -4Y2) = 0 Solving 18 + 6Y + -4Y2 = 0 Solving for variable 'Y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 3Y + -2Y2) = 0 Factor a trinomial. 2((3 + -1Y)(3 + 2Y)) = 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 '(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 = -1.5Solution
Y = {3, -1.5}
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