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Simplifying (3 + -1y)(3y + 5) = 0 Reorder the terms: (3 + -1y)(5 + 3y) = 0 Multiply (3 + -1y) * (5 + 3y) (3(5 + 3y) + -1y * (5 + 3y)) = 0 ((5 * 3 + 3y * 3) + -1y * (5 + 3y)) = 0 ((15 + 9y) + -1y * (5 + 3y)) = 0 (15 + 9y + (5 * -1y + 3y * -1y)) = 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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