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Simplifying (3y + 1)(4 + -1y) = 0 Reorder the terms: (1 + 3y)(4 + -1y) = 0 Multiply (1 + 3y) * (4 + -1y) (1(4 + -1y) + 3y * (4 + -1y)) = 0 ((4 * 1 + -1y * 1) + 3y * (4 + -1y)) = 0 ((4 + -1y) + 3y * (4 + -1y)) = 0 (4 + -1y + (4 * 3y + -1y * 3y)) = 0 (4 + -1y + (12y + -3y2)) = 0 Combine like terms: -1y + 12y = 11y (4 + 11y + -3y2) = 0 Solving 4 + 11y + -3y2 = 0 Solving for variable 'y'. Factor a trinomial. (4 + -1y)(1 + 3y) = 0Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Subproblem 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 = {4, -0.3333333333}
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