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Simplifying 7y2 + -7y + 15 + -13y2 + -7y + 5 = 0 Reorder the terms: 15 + 5 + -7y + -7y + 7y2 + -13y2 = 0 Combine like terms: 15 + 5 = 20 20 + -7y + -7y + 7y2 + -13y2 = 0 Combine like terms: -7y + -7y = -14y 20 + -14y + 7y2 + -13y2 = 0 Combine like terms: 7y2 + -13y2 = -6y2 20 + -14y + -6y2 = 0 Solving 20 + -14y + -6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -7y + -3y2) = 0 Factor a trinomial. 2((1 + -1y)(10 + 3y)) = 0 Ignore the factor 2.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 '(10 + 3y)' equal to zero and attempt to solve: Simplifying 10 + 3y = 0 Solving 10 + 3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3y = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3y = 0 + -10 3y = 0 + -10 Combine like terms: 0 + -10 = -10 3y = -10 Divide each side by '3'. y = -3.333333333 Simplifying y = -3.333333333Solution
y = {1, -3.333333333}
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