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Simplifying (13r + 9)(4r + -12) = 0 Reorder the terms: (9 + 13r)(4r + -12) = 0 Reorder the terms: (9 + 13r)(-12 + 4r) = 0 Multiply (9 + 13r) * (-12 + 4r) (9(-12 + 4r) + 13r * (-12 + 4r)) = 0 ((-12 * 9 + 4r * 9) + 13r * (-12 + 4r)) = 0 ((-108 + 36r) + 13r * (-12 + 4r)) = 0 (-108 + 36r + (-12 * 13r + 4r * 13r)) = 0 (-108 + 36r + (-156r + 52r2)) = 0 Combine like terms: 36r + -156r = -120r (-108 + -120r + 52r2) = 0 Solving -108 + -120r + 52r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -30r + 13r2) = 0 Factor a trinomial. 4((-9 + -13r)(3 + -1r)) = 0 Ignore the factor 4.Subproblem 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 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {-0.6923076923, 3}
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