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Simplifying (4c + 2)(c + 4) = 0 Reorder the terms: (2 + 4c)(c + 4) = 0 Reorder the terms: (2 + 4c)(4 + c) = 0 Multiply (2 + 4c) * (4 + c) (2(4 + c) + 4c * (4 + c)) = 0 ((4 * 2 + c * 2) + 4c * (4 + c)) = 0 ((8 + 2c) + 4c * (4 + c)) = 0 (8 + 2c + (4 * 4c + c * 4c)) = 0 (8 + 2c + (16c + 4c2)) = 0 Combine like terms: 2c + 16c = 18c (8 + 18c + 4c2) = 0 Solving 8 + 18c + 4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9c + 2c2) = 0 Factor a trinomial. 2((4 + c)(1 + 2c)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
Set the factor '(1 + 2c)' equal to zero and attempt to solve: Simplifying 1 + 2c = 0 Solving 1 + 2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2c = 0 + -1 2c = 0 + -1 Combine like terms: 0 + -1 = -1 2c = -1 Divide each side by '2'. c = -0.5 Simplifying c = -0.5Solution
c = {-4, -0.5}
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