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Simplifying 0 = -8(10r2 + -5r) + 8(7r2 + 7r) Reorder the terms: 0 = -8(-5r + 10r2) + 8(7r2 + 7r) 0 = (-5r * -8 + 10r2 * -8) + 8(7r2 + 7r) 0 = (40r + -80r2) + 8(7r2 + 7r) Reorder the terms: 0 = 40r + -80r2 + 8(7r + 7r2) 0 = 40r + -80r2 + (7r * 8 + 7r2 * 8) 0 = 40r + -80r2 + (56r + 56r2) Reorder the terms: 0 = 40r + 56r + -80r2 + 56r2 Combine like terms: 40r + 56r = 96r 0 = 96r + -80r2 + 56r2 Combine like terms: -80r2 + 56r2 = -24r2 0 = 96r + -24r2 Solving 0 = 96r + -24r2 Solving for variable 'r'. Remove the zero: -96r + 24r2 = 96r + -24r2 + -96r + 24r2 Reorder the terms: -96r + 24r2 = 96r + -96r + -24r2 + 24r2 Combine like terms: 96r + -96r = 0 -96r + 24r2 = 0 + -24r2 + 24r2 -96r + 24r2 = -24r2 + 24r2 Combine like terms: -24r2 + 24r2 = 0 -96r + 24r2 = 0 Factor out the Greatest Common Factor (GCF), '24r'. 24r(-4 + r) = 0 Ignore the factor 24.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 '(-4 + r)' equal to zero and attempt to solve: Simplifying -4 + r = 0 Solving -4 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + r = 0 + 4 r = 0 + 4 Combine like terms: 0 + 4 = 4 r = 4 Simplifying r = 4Solution
r = {0, 4}
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