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Simplifying (2y + 5)(y + -2) = 0 Reorder the terms: (5 + 2y)(y + -2) = 0 Reorder the terms: (5 + 2y)(-2 + y) = 0 Multiply (5 + 2y) * (-2 + y) (5(-2 + y) + 2y * (-2 + y)) = 0 ((-2 * 5 + y * 5) + 2y * (-2 + y)) = 0 ((-10 + 5y) + 2y * (-2 + y)) = 0 (-10 + 5y + (-2 * 2y + y * 2y)) = 0 (-10 + 5y + (-4y + 2y2)) = 0 Combine like terms: 5y + -4y = 1y (-10 + 1y + 2y2) = 0 Solving -10 + 1y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -2y)(2 + -1y) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {-2.5, 2}
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