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Simplifying (3y + -1)(2y + 5) = 0 Reorder the terms: (-1 + 3y)(2y + 5) = 0 Reorder the terms: (-1 + 3y)(5 + 2y) = 0 Multiply (-1 + 3y) * (5 + 2y) (-1(5 + 2y) + 3y * (5 + 2y)) = 0 ((5 * -1 + 2y * -1) + 3y * (5 + 2y)) = 0 ((-5 + -2y) + 3y * (5 + 2y)) = 0 (-5 + -2y + (5 * 3y + 2y * 3y)) = 0 (-5 + -2y + (15y + 6y2)) = 0 Combine like terms: -2y + 15y = 13y (-5 + 13y + 6y2) = 0 Solving -5 + 13y + 6y2 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -2y)(1 + -3y) = 0Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 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 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5Subproblem 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 = {-2.5, 0.3333333333}
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