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Simplifying (13r + 9)(4r + -3) = 0 Reorder the terms: (9 + 13r)(4r + -3) = 0 Reorder the terms: (9 + 13r)(-3 + 4r) = 0 Multiply (9 + 13r) * (-3 + 4r) (9(-3 + 4r) + 13r * (-3 + 4r)) = 0 ((-3 * 9 + 4r * 9) + 13r * (-3 + 4r)) = 0 ((-27 + 36r) + 13r * (-3 + 4r)) = 0 (-27 + 36r + (-3 * 13r + 4r * 13r)) = 0 (-27 + 36r + (-39r + 52r2)) = 0 Combine like terms: 36r + -39r = -3r (-27 + -3r + 52r2) = 0 Solving -27 + -3r + 52r2 = 0 Solving for variable 'r'. Factor a trinomial. (-9 + -13r)(3 + -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 '(3 + -4r)' equal to zero and attempt to solve: Simplifying 3 + -4r = 0 Solving 3 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4r = 0 + -3 -4r = 0 + -3 Combine like terms: 0 + -3 = -3 -4r = -3 Divide each side by '-4'. r = 0.75 Simplifying r = 0.75Solution
r = {-0.6923076923, 0.75}
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