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Simplifying (3r + -1)(2r + 5) = 0 Reorder the terms: (-1 + 3r)(2r + 5) = 0 Reorder the terms: (-1 + 3r)(5 + 2r) = 0 Multiply (-1 + 3r) * (5 + 2r) (-1(5 + 2r) + 3r * (5 + 2r)) = 0 ((5 * -1 + 2r * -1) + 3r * (5 + 2r)) = 0 ((-5 + -2r) + 3r * (5 + 2r)) = 0 (-5 + -2r + (5 * 3r + 2r * 3r)) = 0 (-5 + -2r + (15r + 6r2)) = 0 Combine like terms: -2r + 15r = 13r (-5 + 13r + 6r2) = 0 Solving -5 + 13r + 6r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -2r)(1 + -3r) = 0Subproblem 1
Set the factor '(-5 + -2r)' equal to zero and attempt to solve: Simplifying -5 + -2r = 0 Solving -5 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2r = 0 + 5 -2r = 0 + 5 Combine like terms: 0 + 5 = 5 -2r = 5 Divide each side by '-2'. r = -2.5 Simplifying r = -2.5Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve: Simplifying 1 + -3r = 0 Solving 1 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3r = 0 + -1 -3r = 0 + -1 Combine like terms: 0 + -1 = -1 -3r = -1 Divide each side by '-3'. r = 0.3333333333 Simplifying r = 0.3333333333Solution
r = {-2.5, 0.3333333333}
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