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Simplifying 36y2 = 12 + -6y Solving 36y2 = 12 + -6y Solving for variable 'y'. Reorder the terms: -12 + 6y + 36y2 = 12 + -6y + -12 + 6y Reorder the terms: -12 + 6y + 36y2 = 12 + -12 + -6y + 6y Combine like terms: 12 + -12 = 0 -12 + 6y + 36y2 = 0 + -6y + 6y -12 + 6y + 36y2 = -6y + 6y Combine like terms: -6y + 6y = 0 -12 + 6y + 36y2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + y + 6y2) = 0 Factor a trinomial. 6((-2 + -3y)(1 + -2y)) = 0 Ignore the factor 6.Subproblem 1
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 = -0.6666666667Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 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 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5Solution
y = {-0.6666666667, 0.5}
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