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Simplifying 2y3 + 4y2 = 3y2 + 3y Reorder the terms: 4y2 + 2y3 = 3y2 + 3y Reorder the terms: 4y2 + 2y3 = 3y + 3y2 Solving 4y2 + 2y3 = 3y + 3y2 Solving for variable 'y'. Reorder the terms: -3y + 4y2 + -3y2 + 2y3 = 3y + 3y2 + -3y + -3y2 Combine like terms: 4y2 + -3y2 = 1y2 -3y + 1y2 + 2y3 = 3y + 3y2 + -3y + -3y2 Reorder the terms: -3y + 1y2 + 2y3 = 3y + -3y + 3y2 + -3y2 Combine like terms: 3y + -3y = 0 -3y + 1y2 + 2y3 = 0 + 3y2 + -3y2 -3y + 1y2 + 2y3 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -3y + 1y2 + 2y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-3 + y + 2y2) = 0 Factor a trinomial. y((-3 + -2y)(1 + -1y)) = 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 '(-3 + -2y)' equal to zero and attempt to solve: Simplifying -3 + -2y = 0 Solving -3 + -2y = 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 + -2y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2y = 0 + 3 -2y = 0 + 3 Combine like terms: 0 + 3 = 3 -2y = 3 Divide each side by '-2'. y = -1.5 Simplifying y = -1.5Subproblem 3
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 = 1Solution
y = {0, -1.5, 1}
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