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Simplifying 10y2 = 75 + -35y Solving 10y2 = 75 + -35y Solving for variable 'y'. Reorder the terms: -75 + 35y + 10y2 = 75 + -35y + -75 + 35y Reorder the terms: -75 + 35y + 10y2 = 75 + -75 + -35y + 35y Combine like terms: 75 + -75 = 0 -75 + 35y + 10y2 = 0 + -35y + 35y -75 + 35y + 10y2 = -35y + 35y Combine like terms: -35y + 35y = 0 -75 + 35y + 10y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + 7y + 2y2) = 0 Factor a trinomial. 5((-5 + -1y)(3 + -2y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve: Simplifying -5 + -1y = 0 Solving -5 + -1y = 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 + -1y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y = 0 + 5 -1y = 0 + 5 Combine like terms: 0 + 5 = 5 -1y = 5 Divide each side by '-1'. y = -5 Simplifying y = -5Subproblem 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 = {-5, 1.5}
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