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Simplifying 30y + 24y2 = 75 Solving 30y + 24y2 = 75 Solving for variable 'y'. Reorder the terms: -75 + 30y + 24y2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 30y + 24y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 10y + 8y2) = 0 Factor a trinomial. 3((-5 + -2y)(5 + -4y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 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 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5Subproblem 2
Set the factor '(5 + -4y)' equal to zero and attempt to solve: Simplifying 5 + -4y = 0 Solving 5 + -4y = 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 + -4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4y = 0 + -5 -4y = 0 + -5 Combine like terms: 0 + -5 = -5 -4y = -5 Divide each side by '-4'. y = 1.25 Simplifying y = 1.25Solution
y = {-2.5, 1.25}
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