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Simplifying (5r + 7)(3r + 4) = 0 Reorder the terms: (7 + 5r)(3r + 4) = 0 Reorder the terms: (7 + 5r)(4 + 3r) = 0 Multiply (7 + 5r) * (4 + 3r) (7(4 + 3r) + 5r * (4 + 3r)) = 0 ((4 * 7 + 3r * 7) + 5r * (4 + 3r)) = 0 ((28 + 21r) + 5r * (4 + 3r)) = 0 (28 + 21r + (4 * 5r + 3r * 5r)) = 0 (28 + 21r + (20r + 15r2)) = 0 Combine like terms: 21r + 20r = 41r (28 + 41r + 15r2) = 0 Solving 28 + 41r + 15r2 = 0 Solving for variable 'r'. Factor a trinomial. (7 + 5r)(4 + 3r) = 0Subproblem 1
Set the factor '(7 + 5r)' equal to zero and attempt to solve: Simplifying 7 + 5r = 0 Solving 7 + 5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5r = 0 + -7 5r = 0 + -7 Combine like terms: 0 + -7 = -7 5r = -7 Divide each side by '5'. r = -1.4 Simplifying r = -1.4Subproblem 2
Set the factor '(4 + 3r)' equal to zero and attempt to solve: Simplifying 4 + 3r = 0 Solving 4 + 3r = 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 + 3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3r = 0 + -4 3r = 0 + -4 Combine like terms: 0 + -4 = -4 3r = -4 Divide each side by '3'. r = -1.333333333 Simplifying r = -1.333333333Solution
r = {-1.4, -1.333333333}
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