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Simplifying (4 + -1y)(2y + 5) = 0 Reorder the terms: (4 + -1y)(5 + 2y) = 0 Multiply (4 + -1y) * (5 + 2y) (4(5 + 2y) + -1y * (5 + 2y)) = 0 ((5 * 4 + 2y * 4) + -1y * (5 + 2y)) = 0 ((20 + 8y) + -1y * (5 + 2y)) = 0 (20 + 8y + (5 * -1y + 2y * -1y)) = 0 (20 + 8y + (-5y + -2y2)) = 0 Combine like terms: 8y + -5y = 3y (20 + 3y + -2y2) = 0 Solving 20 + 3y + -2y2 = 0 Solving for variable 'y'. Factor a trinomial. (4 + -1y)(5 + 2y) = 0Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Subproblem 2
Set the factor '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5Solution
y = {4, -2.5}
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