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Simplifying 5y(2y + 1) + -3y(2y + 1) = 0 Reorder the terms: 5y(1 + 2y) + -3y(2y + 1) = 0 (1 * 5y + 2y * 5y) + -3y(2y + 1) = 0 (5y + 10y2) + -3y(2y + 1) = 0 Reorder the terms: 5y + 10y2 + -3y(1 + 2y) = 0 5y + 10y2 + (1 * -3y + 2y * -3y) = 0 5y + 10y2 + (-3y + -6y2) = 0 Reorder the terms: 5y + -3y + 10y2 + -6y2 = 0 Combine like terms: 5y + -3y = 2y 2y + 10y2 + -6y2 = 0 Combine like terms: 10y2 + -6y2 = 4y2 2y + 4y2 = 0 Solving 2y + 4y2 = 0 Solving for variable 'y'. 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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