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Simplifying 45r2 = 9 + -12r Solving 45r2 = 9 + -12r Solving for variable 'r'. Reorder the terms: -9 + 12r + 45r2 = 9 + -12r + -9 + 12r Reorder the terms: -9 + 12r + 45r2 = 9 + -9 + -12r + 12r Combine like terms: 9 + -9 = 0 -9 + 12r + 45r2 = 0 + -12r + 12r -9 + 12r + 45r2 = -12r + 12r Combine like terms: -12r + 12r = 0 -9 + 12r + 45r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 4r + 15r2) = 0 Factor a trinomial. 3((-3 + -5r)(1 + -3r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -5r)' equal to zero and attempt to solve: Simplifying -3 + -5r = 0 Solving -3 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5r = 0 + 3 -5r = 0 + 3 Combine like terms: 0 + 3 = 3 -5r = 3 Divide each side by '-5'. r = -0.6 Simplifying r = -0.6Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve: Simplifying 1 + -3r = 0 Solving 1 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3r = 0 + -1 -3r = 0 + -1 Combine like terms: 0 + -1 = -1 -3r = -1 Divide each side by '-3'. r = 0.3333333333 Simplifying r = 0.3333333333Solution
r = {-0.6, 0.3333333333}
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