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Simplifying 6y2 + -5y + 12 + -14y2 + -5y + 6 = 0 Reorder the terms: 12 + 6 + -5y + -5y + 6y2 + -14y2 = 0 Combine like terms: 12 + 6 = 18 18 + -5y + -5y + 6y2 + -14y2 = 0 Combine like terms: -5y + -5y = -10y 18 + -10y + 6y2 + -14y2 = 0 Combine like terms: 6y2 + -14y2 = -8y2 18 + -10y + -8y2 = 0 Solving 18 + -10y + -8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -5y + -4y2) = 0 Factor a trinomial. 2((1 + -1y)(9 + 4y)) = 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 '(9 + 4y)' equal to zero and attempt to solve: Simplifying 9 + 4y = 0 Solving 9 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4y = 0 + -9 4y = 0 + -9 Combine like terms: 0 + -9 = -9 4y = -9 Divide each side by '4'. y = -2.25 Simplifying y = -2.25Solution
y = {1, -2.25}
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