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Simplifying 12y = 9y2 + 3 Reorder the terms: 12y = 3 + 9y2 Solving 12y = 3 + 9y2 Solving for variable 'y'. Reorder the terms: -3 + 12y + -9y2 = 3 + 9y2 + -3 + -9y2 Reorder the terms: -3 + 12y + -9y2 = 3 + -3 + 9y2 + -9y2 Combine like terms: 3 + -3 = 0 -3 + 12y + -9y2 = 0 + 9y2 + -9y2 -3 + 12y + -9y2 = 9y2 + -9y2 Combine like terms: 9y2 + -9y2 = 0 -3 + 12y + -9y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 4y + -3y2) = 0 Factor a trinomial. 3((-1 + y)(1 + -3y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + y)' equal to zero and attempt to solve: Simplifying -1 + y = 0 Solving -1 + y = 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 + y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + y = 0 + 1 y = 0 + 1 Combine like terms: 0 + 1 = 1 y = 1 Simplifying y = 1Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 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 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Solution
y = {1, 0.3333333333}
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