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Simplifying y3 + -2y2 + -3y = y3 + 1 Reorder the terms: -3y + -2y2 + y3 = y3 + 1 Reorder the terms: -3y + -2y2 + y3 = 1 + y3 Add '-1y3' to each side of the equation. -3y + -2y2 + y3 + -1y3 = 1 + y3 + -1y3 Combine like terms: y3 + -1y3 = 0 -3y + -2y2 + 0 = 1 + y3 + -1y3 -3y + -2y2 = 1 + y3 + -1y3 Combine like terms: y3 + -1y3 = 0 -3y + -2y2 = 1 + 0 -3y + -2y2 = 1 Solving -3y + -2y2 = 1 Solving for variable 'y'. Reorder the terms: -1 + -3y + -2y2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -3y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 3y + 2y2) = 0 Factor a trinomial. -1((1 + y)(1 + 2y)) = 0 Ignore the factor -1.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 + 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 = {-1, -0.5}
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