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Simplifying (2y + -9)(5 + y) = 0 Reorder the terms: (-9 + 2y)(5 + y) = 0 Multiply (-9 + 2y) * (5 + y) (-9(5 + y) + 2y * (5 + y)) = 0 ((5 * -9 + y * -9) + 2y * (5 + y)) = 0 ((-45 + -9y) + 2y * (5 + y)) = 0 (-45 + -9y + (5 * 2y + y * 2y)) = 0 (-45 + -9y + (10y + 2y2)) = 0 Combine like terms: -9y + 10y = 1y (-45 + 1y + 2y2) = 0 Solving -45 + 1y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -1y)(9 + -2y) = 0Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve: Simplifying -5 + -1y = 0 Solving -5 + -1y = 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 + -1y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y = 0 + 5 -1y = 0 + 5 Combine like terms: 0 + 5 = 5 -1y = 5 Divide each side by '-1'. y = -5 Simplifying y = -5Subproblem 2
Set the factor '(9 + -2y)' equal to zero and attempt to solve: Simplifying 9 + -2y = 0 Solving 9 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2y = 0 + -9 -2y = 0 + -9 Combine like terms: 0 + -9 = -9 -2y = -9 Divide each side by '-2'. y = 4.5 Simplifying y = 4.5Solution
y = {-5, 4.5}
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