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Simplifying 2y3 + -1y2 = 4y2 + 3y Reorder the terms: -1y2 + 2y3 = 4y2 + 3y Reorder the terms: -1y2 + 2y3 = 3y + 4y2 Solving -1y2 + 2y3 = 3y + 4y2 Solving for variable 'y'. Reorder the terms: -3y + -1y2 + -4y2 + 2y3 = 3y + 4y2 + -3y + -4y2 Combine like terms: -1y2 + -4y2 = -5y2 -3y + -5y2 + 2y3 = 3y + 4y2 + -3y + -4y2 Reorder the terms: -3y + -5y2 + 2y3 = 3y + -3y + 4y2 + -4y2 Combine like terms: 3y + -3y = 0 -3y + -5y2 + 2y3 = 0 + 4y2 + -4y2 -3y + -5y2 + 2y3 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -3y + -5y2 + 2y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-3 + -5y + 2y2) = 0 Factor a trinomial. y((-1 + -2y)(3 + -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 '(-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 = -0.5Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 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 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {0, -0.5, 3}
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