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Simplifying (3y + -1)(y + 2) = 76 Reorder the terms: (-1 + 3y)(y + 2) = 76 Reorder the terms: (-1 + 3y)(2 + y) = 76 Multiply (-1 + 3y) * (2 + y) (-1(2 + y) + 3y * (2 + y)) = 76 ((2 * -1 + y * -1) + 3y * (2 + y)) = 76 ((-2 + -1y) + 3y * (2 + y)) = 76 (-2 + -1y + (2 * 3y + y * 3y)) = 76 (-2 + -1y + (6y + 3y2)) = 76 Combine like terms: -1y + 6y = 5y (-2 + 5y + 3y2) = 76 Solving -2 + 5y + 3y2 = 76 Solving for variable 'y'. Reorder the terms: -2 + -76 + 5y + 3y2 = 76 + -76 Combine like terms: -2 + -76 = -78 -78 + 5y + 3y2 = 76 + -76 Combine like terms: 76 + -76 = 0 -78 + 5y + 3y2 = 0 Factor a trinomial. (-6 + -1y)(13 + -3y) = 0Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve: Simplifying -6 + -1y = 0 Solving -6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1y = 0 + 6 -1y = 0 + 6 Combine like terms: 0 + 6 = 6 -1y = 6 Divide each side by '-1'. y = -6 Simplifying y = -6Subproblem 2
Set the factor '(13 + -3y)' equal to zero and attempt to solve: Simplifying 13 + -3y = 0 Solving 13 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3y = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3y = 0 + -13 -3y = 0 + -13 Combine like terms: 0 + -13 = -13 -3y = -13 Divide each side by '-3'. y = 4.333333333 Simplifying y = 4.333333333Solution
y = {-6, 4.333333333}
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