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Simplifying (4r + -9)(3r + -17) = 0 Reorder the terms: (-9 + 4r)(3r + -17) = 0 Reorder the terms: (-9 + 4r)(-17 + 3r) = 0 Multiply (-9 + 4r) * (-17 + 3r) (-9(-17 + 3r) + 4r * (-17 + 3r)) = 0 ((-17 * -9 + 3r * -9) + 4r * (-17 + 3r)) = 0 ((153 + -27r) + 4r * (-17 + 3r)) = 0 (153 + -27r + (-17 * 4r + 3r * 4r)) = 0 (153 + -27r + (-68r + 12r2)) = 0 Combine like terms: -27r + -68r = -95r (153 + -95r + 12r2) = 0 Solving 153 + -95r + 12r2 = 0 Solving for variable 'r'. Factor a trinomial. (9 + -4r)(17 + -3r) = 0Subproblem 1
Set the factor '(9 + -4r)' equal to zero and attempt to solve: Simplifying 9 + -4r = 0 Solving 9 + -4r = 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 + -4r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4r = 0 + -9 -4r = 0 + -9 Combine like terms: 0 + -9 = -9 -4r = -9 Divide each side by '-4'. r = 2.25 Simplifying r = 2.25Subproblem 2
Set the factor '(17 + -3r)' equal to zero and attempt to solve: Simplifying 17 + -3r = 0 Solving 17 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3r = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3r = 0 + -17 -3r = 0 + -17 Combine like terms: 0 + -17 = -17 -3r = -17 Divide each side by '-3'. r = 5.666666667 Simplifying r = 5.666666667Solution
r = {2.25, 5.666666667}
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