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Simplifying (3y + 5)(2y + -1) = 0 Reorder the terms: (5 + 3y)(2y + -1) = 0 Reorder the terms: (5 + 3y)(-1 + 2y) = 0 Multiply (5 + 3y) * (-1 + 2y) (5(-1 + 2y) + 3y * (-1 + 2y)) = 0 ((-1 * 5 + 2y * 5) + 3y * (-1 + 2y)) = 0 ((-5 + 10y) + 3y * (-1 + 2y)) = 0 (-5 + 10y + (-1 * 3y + 2y * 3y)) = 0 (-5 + 10y + (-3y + 6y2)) = 0 Combine like terms: 10y + -3y = 7y (-5 + 7y + 6y2) = 0 Solving -5 + 7y + 6y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -3y)(1 + -2y) = 0Subproblem 1
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 = -1.666666667Subproblem 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 = {-1.666666667, 0.5}
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