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Simplifying (7r + -4)(3r + -9) = 0 Reorder the terms: (-4 + 7r)(3r + -9) = 0 Reorder the terms: (-4 + 7r)(-9 + 3r) = 0 Multiply (-4 + 7r) * (-9 + 3r) (-4(-9 + 3r) + 7r * (-9 + 3r)) = 0 ((-9 * -4 + 3r * -4) + 7r * (-9 + 3r)) = 0 ((36 + -12r) + 7r * (-9 + 3r)) = 0 (36 + -12r + (-9 * 7r + 3r * 7r)) = 0 (36 + -12r + (-63r + 21r2)) = 0 Combine like terms: -12r + -63r = -75r (36 + -75r + 21r2) = 0 Solving 36 + -75r + 21r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -25r + 7r2) = 0 Factor a trinomial. 3((4 + -7r)(3 + -1r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -7r)' equal to zero and attempt to solve: Simplifying 4 + -7r = 0 Solving 4 + -7r = 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 + -7r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7r = 0 + -4 -7r = 0 + -4 Combine like terms: 0 + -4 = -4 -7r = -4 Divide each side by '-7'. r = 0.5714285714 Simplifying r = 0.5714285714Subproblem 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 = {0.5714285714, 3}
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