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Simplifying 6r(2r + 3) + r(3r + 4) = 0 Reorder the terms: 6r(3 + 2r) + r(3r + 4) = 0 (3 * 6r + 2r * 6r) + r(3r + 4) = 0 (18r + 12r2) + r(3r + 4) = 0 Reorder the terms: 18r + 12r2 + r(4 + 3r) = 0 18r + 12r2 + (4 * r + 3r * r) = 0 18r + 12r2 + (4r + 3r2) = 0 Reorder the terms: 18r + 4r + 12r2 + 3r2 = 0 Combine like terms: 18r + 4r = 22r 22r + 12r2 + 3r2 = 0 Combine like terms: 12r2 + 3r2 = 15r2 22r + 15r2 = 0 Solving 22r + 15r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(22 + 15r) = 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 '(22 + 15r)' equal to zero and attempt to solve: Simplifying 22 + 15r = 0 Solving 22 + 15r = 0 Move all terms containing r to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + 15r = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 15r = 0 + -22 15r = 0 + -22 Combine like terms: 0 + -22 = -22 15r = -22 Divide each side by '15'. r = -1.466666667 Simplifying r = -1.466666667Solution
r = {0, -1.466666667}
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