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Simplifying (10 + 5y)(2y + -3) = 0 Reorder the terms: (10 + 5y)(-3 + 2y) = 0 Multiply (10 + 5y) * (-3 + 2y) (10(-3 + 2y) + 5y * (-3 + 2y)) = 0 ((-3 * 10 + 2y * 10) + 5y * (-3 + 2y)) = 0 ((-30 + 20y) + 5y * (-3 + 2y)) = 0 (-30 + 20y + (-3 * 5y + 2y * 5y)) = 0 (-30 + 20y + (-15y + 10y2)) = 0 Combine like terms: 20y + -15y = 5y (-30 + 5y + 10y2) = 0 Solving -30 + 5y + 10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + y + 2y2) = 0 Factor a trinomial. 5((-2 + -1y)(3 + -2y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 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 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2Subproblem 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 = {-2, 1.5}
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