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