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Simplifying 6r2 = 10 + -7r Solving 6r2 = 10 + -7r Solving for variable 'r'. Reorder the terms: -10 + 7r + 6r2 = 10 + -7r + -10 + 7r Reorder the terms: -10 + 7r + 6r2 = 10 + -10 + -7r + 7r Combine like terms: 10 + -10 = 0 -10 + 7r + 6r2 = 0 + -7r + 7r -10 + 7r + 6r2 = -7r + 7r Combine like terms: -7r + 7r = 0 -10 + 7r + 6r2 = 0 Factor a trinomial. (-2 + -1r)(5 + -6r) = 0Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 2
Set the factor '(5 + -6r)' equal to zero and attempt to solve: Simplifying 5 + -6r = 0 Solving 5 + -6r = 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 + -6r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6r = 0 + -5 -6r = 0 + -5 Combine like terms: 0 + -5 = -5 -6r = -5 Divide each side by '-6'. r = 0.8333333333 Simplifying r = 0.8333333333Solution
r = {-2, 0.8333333333}
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