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Simplifying (3r + -4)(r + 5) = 0 Reorder the terms: (-4 + 3r)(r + 5) = 0 Reorder the terms: (-4 + 3r)(5 + r) = 0 Multiply (-4 + 3r) * (5 + r) (-4(5 + r) + 3r * (5 + r)) = 0 ((5 * -4 + r * -4) + 3r * (5 + r)) = 0 ((-20 + -4r) + 3r * (5 + r)) = 0 (-20 + -4r + (5 * 3r + r * 3r)) = 0 (-20 + -4r + (15r + 3r2)) = 0 Combine like terms: -4r + 15r = 11r (-20 + 11r + 3r2) = 0 Solving -20 + 11r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -1r)(4 + -3r) = 0Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 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 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333Solution
r = {-5, 1.333333333}
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