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Simplifying (3y + -5)(2y + 6) = 0 Reorder the terms: (-5 + 3y)(2y + 6) = 0 Reorder the terms: (-5 + 3y)(6 + 2y) = 0 Multiply (-5 + 3y) * (6 + 2y) (-5(6 + 2y) + 3y * (6 + 2y)) = 0 ((6 * -5 + 2y * -5) + 3y * (6 + 2y)) = 0 ((-30 + -10y) + 3y * (6 + 2y)) = 0 (-30 + -10y + (6 * 3y + 2y * 3y)) = 0 (-30 + -10y + (18y + 6y2)) = 0 Combine like terms: -10y + 18y = 8y (-30 + 8y + 6y2) = 0 Solving -30 + 8y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 4y + 3y2) = 0 Factor a trinomial. 2((-3 + -1y)(5 + -3y)) = 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 '(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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