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Simplifying 5y2 + -5y + 15 + -15y2 + -5y + 5 = 0 Reorder the terms: 15 + 5 + -5y + -5y + 5y2 + -15y2 = 0 Combine like terms: 15 + 5 = 20 20 + -5y + -5y + 5y2 + -15y2 = 0 Combine like terms: -5y + -5y = -10y 20 + -10y + 5y2 + -15y2 = 0 Combine like terms: 5y2 + -15y2 = -10y2 20 + -10y + -10y2 = 0 Solving 20 + -10y + -10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '10'. 10(2 + -1y + -1y2) = 0 Factor a trinomial. 10((1 + -1y)(2 + y)) = 0 Ignore the factor 10.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 '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Solution
y = {1, -2}
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