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Simplifying (3r + -2)(4r + -4) = 0 Reorder the terms: (-2 + 3r)(4r + -4) = 0 Reorder the terms: (-2 + 3r)(-4 + 4r) = 0 Multiply (-2 + 3r) * (-4 + 4r) (-2(-4 + 4r) + 3r * (-4 + 4r)) = 0 ((-4 * -2 + 4r * -2) + 3r * (-4 + 4r)) = 0 ((8 + -8r) + 3r * (-4 + 4r)) = 0 (8 + -8r + (-4 * 3r + 4r * 3r)) = 0 (8 + -8r + (-12r + 12r2)) = 0 Combine like terms: -8r + -12r = -20r (8 + -20r + 12r2) = 0 Solving 8 + -20r + 12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -5r + 3r2) = 0 Factor a trinomial. 4((2 + -3r)(1 + -1r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -3r)' equal to zero and attempt to solve: Simplifying 2 + -3r = 0 Solving 2 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3r = 0 + -2 -3r = 0 + -2 Combine like terms: 0 + -2 = -2 -3r = -2 Divide each side by '-3'. r = 0.6666666667 Simplifying r = 0.6666666667Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 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 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {0.6666666667, 1}
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