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Simplifying -8 = (3r + 1)(r + 4) Reorder the terms: -8 = (1 + 3r)(r + 4) Reorder the terms: -8 = (1 + 3r)(4 + r) Multiply (1 + 3r) * (4 + r) -8 = (1(4 + r) + 3r * (4 + r)) -8 = ((4 * 1 + r * 1) + 3r * (4 + r)) -8 = ((4 + 1r) + 3r * (4 + r)) -8 = (4 + 1r + (4 * 3r + r * 3r)) -8 = (4 + 1r + (12r + 3r2)) Combine like terms: 1r + 12r = 13r -8 = (4 + 13r + 3r2) Solving -8 = 4 + 13r + 3r2 Solving for variable 'r'. Combine like terms: -8 + -4 = -12 -12 + -13r + -3r2 = 4 + 13r + 3r2 + -4 + -13r + -3r2 Reorder the terms: -12 + -13r + -3r2 = 4 + -4 + 13r + -13r + 3r2 + -3r2 Combine like terms: 4 + -4 = 0 -12 + -13r + -3r2 = 0 + 13r + -13r + 3r2 + -3r2 -12 + -13r + -3r2 = 13r + -13r + 3r2 + -3r2 Combine like terms: 13r + -13r = 0 -12 + -13r + -3r2 = 0 + 3r2 + -3r2 -12 + -13r + -3r2 = 3r2 + -3r2 Combine like terms: 3r2 + -3r2 = 0 -12 + -13r + -3r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 13r + 3r2) = 0 Factor a trinomial. -1((3 + r)(4 + 3r)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve: Simplifying 3 + r = 0 Solving 3 + r = 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 + r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r = 0 + -3 r = 0 + -3 Combine like terms: 0 + -3 = -3 r = -3 Simplifying r = -3Subproblem 2
Set the factor '(4 + 3r)' equal to zero and attempt to solve: Simplifying 4 + 3r = 0 Solving 4 + 3r = 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 + 3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3r = 0 + -4 3r = 0 + -4 Combine like terms: 0 + -4 = -4 3r = -4 Divide each side by '3'. r = -1.333333333 Simplifying r = -1.333333333Solution
r = {-3, -1.333333333}
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