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Simplifying (r + 4)(r + 81) = 0 Reorder the terms: (4 + r)(r + 81) = 0 Reorder the terms: (4 + r)(81 + r) = 0 Multiply (4 + r) * (81 + r) (4(81 + r) + r(81 + r)) = 0 ((81 * 4 + r * 4) + r(81 + r)) = 0 ((324 + 4r) + r(81 + r)) = 0 (324 + 4r + (81 * r + r * r)) = 0 (324 + 4r + (81r + r2)) = 0 Combine like terms: 4r + 81r = 85r (324 + 85r + r2) = 0 Solving 324 + 85r + r2 = 0 Solving for variable 'r'. Factor a trinomial. (81 + r)(4 + r) = 0Subproblem 1
Set the factor '(81 + r)' equal to zero and attempt to solve: Simplifying 81 + r = 0 Solving 81 + r = 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 + r = 0 + -81 Combine like terms: 81 + -81 = 0 0 + r = 0 + -81 r = 0 + -81 Combine like terms: 0 + -81 = -81 r = -81 Simplifying r = -81Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 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 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4Solution
r = {-81, -4}
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