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Simplifying (r + -9)(r + 81) = 0 Reorder the terms: (-9 + r)(r + 81) = 0 Reorder the terms: (-9 + r)(81 + r) = 0 Multiply (-9 + r) * (81 + r) (-9(81 + r) + r(81 + r)) = 0 ((81 * -9 + r * -9) + r(81 + r)) = 0 ((-729 + -9r) + r(81 + r)) = 0 (-729 + -9r + (81 * r + r * r)) = 0 (-729 + -9r + (81r + r2)) = 0 Combine like terms: -9r + 81r = 72r (-729 + 72r + r2) = 0 Solving -729 + 72r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (-81 + -1r)(9 + -1r) = 0Subproblem 1
Set the factor '(-81 + -1r)' equal to zero and attempt to solve: Simplifying -81 + -1r = 0 Solving -81 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + -1r = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -1r = 0 + 81 -1r = 0 + 81 Combine like terms: 0 + 81 = 81 -1r = 81 Divide each side by '-1'. r = -81 Simplifying r = -81Subproblem 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 = {-81, 9}
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