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Simplifying 0 = r2 + 3r + -40 Reorder the terms: 0 = -40 + 3r + r2 Solving 0 = -40 + 3r + r2 Solving for variable 'r'. Combine like terms: 0 + 40 = 40 40 + -3r + -1r2 = -40 + 3r + r2 + 40 + -3r + -1r2 Reorder the terms: 40 + -3r + -1r2 = -40 + 40 + 3r + -3r + r2 + -1r2 Combine like terms: -40 + 40 = 0 40 + -3r + -1r2 = 0 + 3r + -3r + r2 + -1r2 40 + -3r + -1r2 = 3r + -3r + r2 + -1r2 Combine like terms: 3r + -3r = 0 40 + -3r + -1r2 = 0 + r2 + -1r2 40 + -3r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 40 + -3r + -1r2 = 0 Factor a trinomial. (5 + -1r)(8 + r) = 0Subproblem 1
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 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 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Subproblem 2
Set the factor '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8Solution
r = {5, -8}
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