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Simplifying 3y3 + 12y2 = y2 + 4y Reorder the terms: 12y2 + 3y3 = y2 + 4y Reorder the terms: 12y2 + 3y3 = 4y + y2 Solving 12y2 + 3y3 = 4y + y2 Solving for variable 'y'. Reorder the terms: -4y + 12y2 + -1y2 + 3y3 = 4y + y2 + -4y + -1y2 Combine like terms: 12y2 + -1y2 = 11y2 -4y + 11y2 + 3y3 = 4y + y2 + -4y + -1y2 Reorder the terms: -4y + 11y2 + 3y3 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 -4y + 11y2 + 3y3 = 0 + y2 + -1y2 -4y + 11y2 + 3y3 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -4y + 11y2 + 3y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-4 + 11y + 3y2) = 0 Factor a trinomial. y((-4 + -1y)(1 + -3y)) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4Subproblem 3
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 = {0, -4, 0.3333333333}
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