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Simplifying 3r(r + -5) + -2r(3r + -1) = 0 Reorder the terms: 3r(-5 + r) + -2r(3r + -1) = 0 (-5 * 3r + r * 3r) + -2r(3r + -1) = 0 (-15r + 3r2) + -2r(3r + -1) = 0 Reorder the terms: -15r + 3r2 + -2r(-1 + 3r) = 0 -15r + 3r2 + (-1 * -2r + 3r * -2r) = 0 -15r + 3r2 + (2r + -6r2) = 0 Reorder the terms: -15r + 2r + 3r2 + -6r2 = 0 Combine like terms: -15r + 2r = -13r -13r + 3r2 + -6r2 = 0 Combine like terms: 3r2 + -6r2 = -3r2 -13r + -3r2 = 0 Solving -13r + -3r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '-1r'. -1r(13 + 3r) = 0 Ignore the factor -1.Subproblem 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 '(13 + 3r)' equal to zero and attempt to solve: Simplifying 13 + 3r = 0 Solving 13 + 3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 3r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3r = 0 + -13 3r = 0 + -13 Combine like terms: 0 + -13 = -13 3r = -13 Divide each side by '3'. r = -4.333333333 Simplifying r = -4.333333333Solution
r = {0, -4.333333333}
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