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Simplifying (r + 4)(3r + 3)(2r) = 0 Reorder the terms: (4 + r)(3r + 3)(2r) = 0 Reorder the terms: (4 + r)(3 + 3r)(2r) = 0 Remove parenthesis around (2r) (4 + r)(3 + 3r) * 2r = 0 Reorder the terms for easier multiplication: 2r(4 + r)(3 + 3r) = 0 Multiply (4 + r) * (3 + 3r) 2r(4(3 + 3r) + r(3 + 3r)) = 0 2r((3 * 4 + 3r * 4) + r(3 + 3r)) = 0 2r((12 + 12r) + r(3 + 3r)) = 0 2r(12 + 12r + (3 * r + 3r * r)) = 0 2r(12 + 12r + (3r + 3r2)) = 0 Combine like terms: 12r + 3r = 15r 2r(12 + 15r + 3r2) = 0 (12 * 2r + 15r * 2r + 3r2 * 2r) = 0 (24r + 30r2 + 6r3) = 0 Solving 24r + 30r2 + 6r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '6r'. 6r(4 + 5r + r2) = 0 Factor a trinomial. 6r((4 + r)(1 + r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 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 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4Subproblem 3
Set the factor '(1 + r)' equal to zero and attempt to solve: Simplifying 1 + r = 0 Solving 1 + r = 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 + r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r = 0 + -1 r = 0 + -1 Combine like terms: 0 + -1 = -1 r = -1 Simplifying r = -1Solution
r = {0, -4, -1}
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