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Simplifying (4r + -2)(10r + -8) = 0 Reorder the terms: (-2 + 4r)(10r + -8) = 0 Reorder the terms: (-2 + 4r)(-8 + 10r) = 0 Multiply (-2 + 4r) * (-8 + 10r) (-2(-8 + 10r) + 4r * (-8 + 10r)) = 0 ((-8 * -2 + 10r * -2) + 4r * (-8 + 10r)) = 0 ((16 + -20r) + 4r * (-8 + 10r)) = 0 (16 + -20r + (-8 * 4r + 10r * 4r)) = 0 (16 + -20r + (-32r + 40r2)) = 0 Combine like terms: -20r + -32r = -52r (16 + -52r + 40r2) = 0 Solving 16 + -52r + 40r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -13r + 10r2) = 0 Factor a trinomial. 4((1 + -2r)(4 + -5r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Subproblem 2
Set the factor '(4 + -5r)' equal to zero and attempt to solve: Simplifying 4 + -5r = 0 Solving 4 + -5r = 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 + -5r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5r = 0 + -4 -5r = 0 + -4 Combine like terms: 0 + -4 = -4 -5r = -4 Divide each side by '-5'. r = 0.8 Simplifying r = 0.8Solution
r = {0.5, 0.8}
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