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Simplifying 4(3r + 4)(r + 2) = 0 Reorder the terms: 4(4 + 3r)(r + 2) = 0 Reorder the terms: 4(4 + 3r)(2 + r) = 0 Multiply (4 + 3r) * (2 + r) 4(4(2 + r) + 3r * (2 + r)) = 0 4((2 * 4 + r * 4) + 3r * (2 + r)) = 0 4((8 + 4r) + 3r * (2 + r)) = 0 4(8 + 4r + (2 * 3r + r * 3r)) = 0 4(8 + 4r + (6r + 3r2)) = 0 Combine like terms: 4r + 6r = 10r 4(8 + 10r + 3r2) = 0 (8 * 4 + 10r * 4 + 3r2 * 4) = 0 (32 + 40r + 12r2) = 0 Solving 32 + 40r + 12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + 10r + 3r2) = 0 Factor a trinomial. 4((2 + r)(4 + 3r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + r)' equal to zero and attempt to solve: Simplifying 2 + r = 0 Solving 2 + r = 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 + r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + r = 0 + -2 r = 0 + -2 Combine like terms: 0 + -2 = -2 r = -2 Simplifying r = -2Subproblem 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 = {-2, -1.333333333}
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