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Simplifying 2r2 = 6r + 20 Reorder the terms: 2r2 = 20 + 6r Solving 2r2 = 20 + 6r Solving for variable 'r'. Reorder the terms: -20 + -6r + 2r2 = 20 + 6r + -20 + -6r Reorder the terms: -20 + -6r + 2r2 = 20 + -20 + 6r + -6r Combine like terms: 20 + -20 = 0 -20 + -6r + 2r2 = 0 + 6r + -6r -20 + -6r + 2r2 = 6r + -6r Combine like terms: 6r + -6r = 0 -20 + -6r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -3r + r2) = 0 Factor a trinomial. 2((-2 + -1r)(5 + -1r)) = 0 Ignore the factor 2.Subproblem 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 + -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 = 5Solution
r = {-2, 5}
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