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Simplifying (2r + 6)(2r + 4) = 0 Reorder the terms: (6 + 2r)(2r + 4) = 0 Reorder the terms: (6 + 2r)(4 + 2r) = 0 Multiply (6 + 2r) * (4 + 2r) (6(4 + 2r) + 2r * (4 + 2r)) = 0 ((4 * 6 + 2r * 6) + 2r * (4 + 2r)) = 0 ((24 + 12r) + 2r * (4 + 2r)) = 0 (24 + 12r + (4 * 2r + 2r * 2r)) = 0 (24 + 12r + (8r + 4r2)) = 0 Combine like terms: 12r + 8r = 20r (24 + 20r + 4r2) = 0 Solving 24 + 20r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 5r + r2) = 0 Factor a trinomial. 4((3 + r)(2 + r)) = 0 Ignore the factor 4.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 '(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 = -2Solution
r = {-3, -2}
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