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Simplifying (5 + y)(3y + -1) = 0 Reorder the terms: (5 + y)(-1 + 3y) = 0 Multiply (5 + y) * (-1 + 3y) (5(-1 + 3y) + y(-1 + 3y)) = 0 ((-1 * 5 + 3y * 5) + y(-1 + 3y)) = 0 ((-5 + 15y) + y(-1 + 3y)) = 0 (-5 + 15y + (-1 * y + 3y * y)) = 0 (-5 + 15y + (-1y + 3y2)) = 0 Combine like terms: 15y + -1y = 14y (-5 + 14y + 3y2) = 0 Solving -5 + 14y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -1y)(1 + -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 '(1 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Solution
y = {-5, 0.3333333333}
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