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Simplifying (7r + 3)(4r + -12) = 0 Reorder the terms: (3 + 7r)(4r + -12) = 0 Reorder the terms: (3 + 7r)(-12 + 4r) = 0 Multiply (3 + 7r) * (-12 + 4r) (3(-12 + 4r) + 7r * (-12 + 4r)) = 0 ((-12 * 3 + 4r * 3) + 7r * (-12 + 4r)) = 0 ((-36 + 12r) + 7r * (-12 + 4r)) = 0 (-36 + 12r + (-12 * 7r + 4r * 7r)) = 0 (-36 + 12r + (-84r + 28r2)) = 0 Combine like terms: 12r + -84r = -72r (-36 + -72r + 28r2) = 0 Solving -36 + -72r + 28r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -18r + 7r2) = 0 Factor a trinomial. 4((-3 + -7r)(3 + -1r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -7r)' equal to zero and attempt to solve: Simplifying -3 + -7r = 0 Solving -3 + -7r = 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 + -7r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7r = 0 + 3 -7r = 0 + 3 Combine like terms: 0 + 3 = 3 -7r = 3 Divide each side by '-7'. r = -0.4285714286 Simplifying r = -0.4285714286Subproblem 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 = {-0.4285714286, 3}
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