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Simplifying 2r(4r + 8) + -5r(6r + -10) = 0 Reorder the terms: 2r(8 + 4r) + -5r(6r + -10) = 0 (8 * 2r + 4r * 2r) + -5r(6r + -10) = 0 (16r + 8r2) + -5r(6r + -10) = 0 Reorder the terms: 16r + 8r2 + -5r(-10 + 6r) = 0 16r + 8r2 + (-10 * -5r + 6r * -5r) = 0 16r + 8r2 + (50r + -30r2) = 0 Reorder the terms: 16r + 50r + 8r2 + -30r2 = 0 Combine like terms: 16r + 50r = 66r 66r + 8r2 + -30r2 = 0 Combine like terms: 8r2 + -30r2 = -22r2 66r + -22r2 = 0 Solving 66r + -22r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '22r'. 22r(3 + -1r) = 0 Ignore the factor 22.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 '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {0, 3}
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