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Simplifying 4r(3r + 8) + r(4r + 9) = 0 Reorder the terms: 4r(8 + 3r) + r(4r + 9) = 0 (8 * 4r + 3r * 4r) + r(4r + 9) = 0 (32r + 12r2) + r(4r + 9) = 0 Reorder the terms: 32r + 12r2 + r(9 + 4r) = 0 32r + 12r2 + (9 * r + 4r * r) = 0 32r + 12r2 + (9r + 4r2) = 0 Reorder the terms: 32r + 9r + 12r2 + 4r2 = 0 Combine like terms: 32r + 9r = 41r 41r + 12r2 + 4r2 = 0 Combine like terms: 12r2 + 4r2 = 16r2 41r + 16r2 = 0 Solving 41r + 16r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(41 + 16r) = 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 '(41 + 16r)' equal to zero and attempt to solve: Simplifying 41 + 16r = 0 Solving 41 + 16r = 0 Move all terms containing r to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + 16r = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 16r = 0 + -41 16r = 0 + -41 Combine like terms: 0 + -41 = -41 16r = -41 Divide each side by '16'. r = -2.5625 Simplifying r = -2.5625Solution
r = {0, -2.5625}
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