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Simplifying (7 + -1r)(6 + -1r) = 6 Multiply (7 + -1r) * (6 + -1r) (7(6 + -1r) + -1r * (6 + -1r)) = 6 ((6 * 7 + -1r * 7) + -1r * (6 + -1r)) = 6 ((42 + -7r) + -1r * (6 + -1r)) = 6 (42 + -7r + (6 * -1r + -1r * -1r)) = 6 (42 + -7r + (-6r + 1r2)) = 6 Combine like terms: -7r + -6r = -13r (42 + -13r + 1r2) = 6 Solving 42 + -13r + 1r2 = 6 Solving for variable 'r'. Reorder the terms: 42 + -6 + -13r + 1r2 = 6 + -6 Combine like terms: 42 + -6 = 36 36 + -13r + 1r2 = 6 + -6 Combine like terms: 6 + -6 = 0 36 + -13r + 1r2 = 0 Factor a trinomial. (4 + -1r)(9 + -1r) = 0Subproblem 1
Set the factor '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 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 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 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 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {4, 9}
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