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Simplifying 8r2 + -13r + 40 = 7r2 Reorder the terms: 40 + -13r + 8r2 = 7r2 Solving 40 + -13r + 8r2 = 7r2 Solving for variable 'r'. Combine like terms: 8r2 + -7r2 = 1r2 40 + -13r + 1r2 = 7r2 + -7r2 Combine like terms: 7r2 + -7r2 = 0 40 + -13r + 1r2 = 0 Factor a trinomial. (5 + -1r)(8 + -1r) = 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 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 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 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8Solution
r = {5, 8}
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