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Simplifying -5y(y + 2) + 3y(4y + -3) = 0 Reorder the terms: -5y(2 + y) + 3y(4y + -3) = 0 (2 * -5y + y * -5y) + 3y(4y + -3) = 0 (-10y + -5y2) + 3y(4y + -3) = 0 Reorder the terms: -10y + -5y2 + 3y(-3 + 4y) = 0 -10y + -5y2 + (-3 * 3y + 4y * 3y) = 0 -10y + -5y2 + (-9y + 12y2) = 0 Reorder the terms: -10y + -9y + -5y2 + 12y2 = 0 Combine like terms: -10y + -9y = -19y -19y + -5y2 + 12y2 = 0 Combine like terms: -5y2 + 12y2 = 7y2 -19y + 7y2 = 0 Solving -19y + 7y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-19 + 7y) = 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 '(-19 + 7y)' equal to zero and attempt to solve: Simplifying -19 + 7y = 0 Solving -19 + 7y = 0 Move all terms containing y to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 7y = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 7y = 0 + 19 7y = 0 + 19 Combine like terms: 0 + 19 = 19 7y = 19 Divide each side by '7'. y = 2.714285714 Simplifying y = 2.714285714Solution
y = {0, 2.714285714}
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