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Simplifying (3y + 1)(7 + -1y) = 0 Reorder the terms: (1 + 3y)(7 + -1y) = 0 Multiply (1 + 3y) * (7 + -1y) (1(7 + -1y) + 3y * (7 + -1y)) = 0 ((7 * 1 + -1y * 1) + 3y * (7 + -1y)) = 0 ((7 + -1y) + 3y * (7 + -1y)) = 0 (7 + -1y + (7 * 3y + -1y * 3y)) = 0 (7 + -1y + (21y + -3y2)) = 0 Combine like terms: -1y + 21y = 20y (7 + 20y + -3y2) = 0 Solving 7 + 20y + -3y2 = 0 Solving for variable 'y'. Factor a trinomial. (7 + -1y)(1 + 3y) = 0Subproblem 1
Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 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 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7Subproblem 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 = {7, -0.3333333333}
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