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Simplifying 2y(3 + -1y) + -3y(2y + 1) = 0 (3 * 2y + -1y * 2y) + -3y(2y + 1) = 0 (6y + -2y2) + -3y(2y + 1) = 0 Reorder the terms: 6y + -2y2 + -3y(1 + 2y) = 0 6y + -2y2 + (1 * -3y + 2y * -3y) = 0 6y + -2y2 + (-3y + -6y2) = 0 Reorder the terms: 6y + -3y + -2y2 + -6y2 = 0 Combine like terms: 6y + -3y = 3y 3y + -2y2 + -6y2 = 0 Combine like terms: -2y2 + -6y2 = -8y2 3y + -8y2 = 0 Solving 3y + -8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(3 + -8y) = 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 + -8y)' equal to zero and attempt to solve: Simplifying 3 + -8y = 0 Solving 3 + -8y = 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 + -8y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8y = 0 + -3 -8y = 0 + -3 Combine like terms: 0 + -3 = -3 -8y = -3 Divide each side by '-8'. y = 0.375 Simplifying y = 0.375Solution
y = {0, 0.375}
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