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