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Simplifying 6y2 + 18y + -4y = 12 Reorder the terms: 18y + -4y + 6y2 = 12 Combine like terms: 18y + -4y = 14y 14y + 6y2 = 12 Solving 14y + 6y2 = 12 Solving for variable 'y'. Reorder the terms: -12 + 14y + 6y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 14y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 7y + 3y2) = 0 Factor a trinomial. 2((-3 + -1y)(2 + -3y)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 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 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667Solution
y = {-3, 0.6666666667}
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