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Simplifying (3r + -1) * r = 12r + -4 Reorder the terms: (-1 + 3r) * r = 12r + -4 Reorder the terms for easier multiplication: r(-1 + 3r) = 12r + -4 (-1 * r + 3r * r) = 12r + -4 (-1r + 3r2) = 12r + -4 Reorder the terms: -1r + 3r2 = -4 + 12r Solving -1r + 3r2 = -4 + 12r Solving for variable 'r'. Reorder the terms: 4 + -1r + -12r + 3r2 = -4 + 12r + 4 + -12r Combine like terms: -1r + -12r = -13r 4 + -13r + 3r2 = -4 + 12r + 4 + -12r Reorder the terms: 4 + -13r + 3r2 = -4 + 4 + 12r + -12r Combine like terms: -4 + 4 = 0 4 + -13r + 3r2 = 0 + 12r + -12r 4 + -13r + 3r2 = 12r + -12r Combine like terms: 12r + -12r = 0 4 + -13r + 3r2 = 0 Factor a trinomial. (1 + -3r)(4 + -1r) = 0Subproblem 1
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 = 0.3333333333Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 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 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4Solution
r = {0.3333333333, 4}
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