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Simplifying (7r + 5)(2r + 9) = 0 Reorder the terms: (5 + 7r)(2r + 9) = 0 Reorder the terms: (5 + 7r)(9 + 2r) = 0 Multiply (5 + 7r) * (9 + 2r) (5(9 + 2r) + 7r * (9 + 2r)) = 0 ((9 * 5 + 2r * 5) + 7r * (9 + 2r)) = 0 ((45 + 10r) + 7r * (9 + 2r)) = 0 (45 + 10r + (9 * 7r + 2r * 7r)) = 0 (45 + 10r + (63r + 14r2)) = 0 Combine like terms: 10r + 63r = 73r (45 + 73r + 14r2) = 0 Solving 45 + 73r + 14r2 = 0 Solving for variable 'r'. Factor a trinomial. (9 + 2r)(5 + 7r) = 0Subproblem 1
Set the factor '(9 + 2r)' equal to zero and attempt to solve: Simplifying 9 + 2r = 0 Solving 9 + 2r = 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 + 2r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2r = 0 + -9 2r = 0 + -9 Combine like terms: 0 + -9 = -9 2r = -9 Divide each side by '2'. r = -4.5 Simplifying r = -4.5Subproblem 2
Set the factor '(5 + 7r)' equal to zero and attempt to solve: Simplifying 5 + 7r = 0 Solving 5 + 7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 7r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7r = 0 + -5 7r = 0 + -5 Combine like terms: 0 + -5 = -5 7r = -5 Divide each side by '7'. r = -0.7142857143 Simplifying r = -0.7142857143Solution
r = {-4.5, -0.7142857143}
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