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Simplifying (1 + -1y)(3y + 5) = 0 Reorder the terms: (1 + -1y)(5 + 3y) = 0 Multiply (1 + -1y) * (5 + 3y) (1(5 + 3y) + -1y * (5 + 3y)) = 0 ((5 * 1 + 3y * 1) + -1y * (5 + 3y)) = 0 ((5 + 3y) + -1y * (5 + 3y)) = 0 (5 + 3y + (5 * -1y + 3y * -1y)) = 0 (5 + 3y + (-5y + -3y2)) = 0 Combine like terms: 3y + -5y = -2y (5 + -2y + -3y2) = 0 Solving 5 + -2y + -3y2 = 0 Solving for variable 'y'. Factor a trinomial. (1 + -1y)(5 + 3y) = 0Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Subproblem 2
Set the factor '(5 + 3y)' equal to zero and attempt to solve: Simplifying 5 + 3y = 0 Solving 5 + 3y = 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 + 3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3y = 0 + -5 3y = 0 + -5 Combine like terms: 0 + -5 = -5 3y = -5 Divide each side by '3'. y = -1.666666667 Simplifying y = -1.666666667Solution
y = {1, -1.666666667}
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