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