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Simplifying (3y + -7)(y + 5) = 0 Reorder the terms: (-7 + 3y)(y + 5) = 0 Reorder the terms: (-7 + 3y)(5 + y) = 0 Multiply (-7 + 3y) * (5 + y) (-7(5 + y) + 3y * (5 + y)) = 0 ((5 * -7 + y * -7) + 3y * (5 + y)) = 0 ((-35 + -7y) + 3y * (5 + y)) = 0 (-35 + -7y + (5 * 3y + y * 3y)) = 0 (-35 + -7y + (15y + 3y2)) = 0 Combine like terms: -7y + 15y = 8y (-35 + 8y + 3y2) = 0 Solving -35 + 8y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -1y)(7 + -3y) = 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 '(7 + -3y)' equal to zero and attempt to solve: Simplifying 7 + -3y = 0 Solving 7 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3y = 0 + -7 -3y = 0 + -7 Combine like terms: 0 + -7 = -7 -3y = -7 Divide each side by '-3'. y = 2.333333333 Simplifying y = 2.333333333Solution
y = {-5, 2.333333333}
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