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Simplifying (13r + 9)(4r + -5) = 0 Reorder the terms: (9 + 13r)(4r + -5) = 0 Reorder the terms: (9 + 13r)(-5 + 4r) = 0 Multiply (9 + 13r) * (-5 + 4r) (9(-5 + 4r) + 13r * (-5 + 4r)) = 0 ((-5 * 9 + 4r * 9) + 13r * (-5 + 4r)) = 0 ((-45 + 36r) + 13r * (-5 + 4r)) = 0 (-45 + 36r + (-5 * 13r + 4r * 13r)) = 0 (-45 + 36r + (-65r + 52r2)) = 0 Combine like terms: 36r + -65r = -29r (-45 + -29r + 52r2) = 0 Solving -45 + -29r + 52r2 = 0 Solving for variable 'r'. Factor a trinomial. (-9 + -13r)(5 + -4r) = 0Subproblem 1
Set the factor '(-9 + -13r)' equal to zero and attempt to solve: Simplifying -9 + -13r = 0 Solving -9 + -13r = 0 Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -13r = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -13r = 0 + 9 -13r = 0 + 9 Combine like terms: 0 + 9 = 9 -13r = 9 Divide each side by '-13'. r = -0.6923076923 Simplifying r = -0.6923076923Subproblem 2
Set the factor '(5 + -4r)' equal to zero and attempt to solve: Simplifying 5 + -4r = 0 Solving 5 + -4r = 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 + -4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r = 0 + -5 -4r = 0 + -5 Combine like terms: 0 + -5 = -5 -4r = -5 Divide each side by '-4'. r = 1.25 Simplifying r = 1.25Solution
r = {-0.6923076923, 1.25}
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