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Simplifying 0 = y2 + 2y + 3y2 Reorder the terms: 0 = 2y + y2 + 3y2 Combine like terms: y2 + 3y2 = 4y2 0 = 2y + 4y2 Solving 0 = 2y + 4y2 Solving for variable 'y'. Remove the zero: -2y + -4y2 = 2y + 4y2 + -2y + -4y2 Reorder the terms: -2y + -4y2 = 2y + -2y + 4y2 + -4y2 Combine like terms: 2y + -2y = 0 -2y + -4y2 = 0 + 4y2 + -4y2 -2y + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -2y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '-2y'. -2y(1 + 2y) = 0 Ignore the factor -2.Subproblem 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 = -0.5Solution
y = {0, -0.5}
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