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Simplifying 8(c + 4)(c + 8) = 0 Reorder the terms: 8(4 + c)(c + 8) = 0 Reorder the terms: 8(4 + c)(8 + c) = 0 Multiply (4 + c) * (8 + c) 8(4(8 + c) + c(8 + c)) = 0 8((8 * 4 + c * 4) + c(8 + c)) = 0 8((32 + 4c) + c(8 + c)) = 0 8(32 + 4c + (8 * c + c * c)) = 0 8(32 + 4c + (8c + c2)) = 0 Combine like terms: 4c + 8c = 12c 8(32 + 12c + c2) = 0 (32 * 8 + 12c * 8 + c2 * 8) = 0 (256 + 96c + 8c2) = 0 Solving 256 + 96c + 8c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '8'. 8(32 + 12c + c2) = 0 Factor a trinomial. 8((8 + c)(4 + c)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(8 + c)' equal to zero and attempt to solve: Simplifying 8 + c = 0 Solving 8 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + c = 0 + -8 Combine like terms: 8 + -8 = 0 0 + c = 0 + -8 c = 0 + -8 Combine like terms: 0 + -8 = -8 c = -8 Simplifying c = -8Subproblem 2
Set the factor '(4 + c)' equal to zero and attempt to solve: Simplifying 4 + c = 0 Solving 4 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + c = 0 + -4 c = 0 + -4 Combine like terms: 0 + -4 = -4 c = -4 Simplifying c = -4Solution
c = {-8, -4}
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