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Simplifying 54r2 = 21r + 20 Reorder the terms: 54r2 = 20 + 21r Solving 54r2 = 20 + 21r Solving for variable 'r'. Reorder the terms: -20 + -21r + 54r2 = 20 + 21r + -20 + -21r Reorder the terms: -20 + -21r + 54r2 = 20 + -20 + 21r + -21r Combine like terms: 20 + -20 = 0 -20 + -21r + 54r2 = 0 + 21r + -21r -20 + -21r + 54r2 = 21r + -21r Combine like terms: 21r + -21r = 0 -20 + -21r + 54r2 = 0 Factor a trinomial. (-4 + -9r)(5 + -6r) = 0Subproblem 1
Set the factor '(-4 + -9r)' equal to zero and attempt to solve: Simplifying -4 + -9r = 0 Solving -4 + -9r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -9r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -9r = 0 + 4 -9r = 0 + 4 Combine like terms: 0 + 4 = 4 -9r = 4 Divide each side by '-9'. r = -0.4444444444 Simplifying r = -0.4444444444Subproblem 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 = {-0.4444444444, 0.8333333333}
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