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Simplifying 10r2 + 20r + -60 = 7r2 + 12r Reorder the terms: -60 + 20r + 10r2 = 7r2 + 12r Reorder the terms: -60 + 20r + 10r2 = 12r + 7r2 Solving -60 + 20r + 10r2 = 12r + 7r2 Solving for variable 'r'. Reorder the terms: -60 + 20r + -12r + 10r2 + -7r2 = 12r + 7r2 + -12r + -7r2 Combine like terms: 20r + -12r = 8r -60 + 8r + 10r2 + -7r2 = 12r + 7r2 + -12r + -7r2 Combine like terms: 10r2 + -7r2 = 3r2 -60 + 8r + 3r2 = 12r + 7r2 + -12r + -7r2 Reorder the terms: -60 + 8r + 3r2 = 12r + -12r + 7r2 + -7r2 Combine like terms: 12r + -12r = 0 -60 + 8r + 3r2 = 0 + 7r2 + -7r2 -60 + 8r + 3r2 = 7r2 + -7r2 Combine like terms: 7r2 + -7r2 = 0 -60 + 8r + 3r2 = 0 Factor a trinomial. (-6 + -1r)(10 + -3r) = 0Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve: Simplifying -6 + -1r = 0 Solving -6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = 0 + 6 -1r = 0 + 6 Combine like terms: 0 + 6 = 6 -1r = 6 Divide each side by '-1'. r = -6 Simplifying r = -6Subproblem 2
Set the factor '(10 + -3r)' equal to zero and attempt to solve: Simplifying 10 + -3r = 0 Solving 10 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3r = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3r = 0 + -10 -3r = 0 + -10 Combine like terms: 0 + -10 = -10 -3r = -10 Divide each side by '-3'. r = 3.333333333 Simplifying r = 3.333333333Solution
r = {-6, 3.333333333}
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