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Simplifying (2c + 8)(5c + 10) = 0 Reorder the terms: (8 + 2c)(5c + 10) = 0 Reorder the terms: (8 + 2c)(10 + 5c) = 0 Multiply (8 + 2c) * (10 + 5c) (8(10 + 5c) + 2c * (10 + 5c)) = 0 ((10 * 8 + 5c * 8) + 2c * (10 + 5c)) = 0 ((80 + 40c) + 2c * (10 + 5c)) = 0 (80 + 40c + (10 * 2c + 5c * 2c)) = 0 (80 + 40c + (20c + 10c2)) = 0 Combine like terms: 40c + 20c = 60c (80 + 60c + 10c2) = 0 Solving 80 + 60c + 10c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '10'. 10(8 + 6c + c2) = 0 Factor a trinomial. 10((4 + c)(2 + c)) = 0 Ignore the factor 10.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 '(2 + c)' equal to zero and attempt to solve: Simplifying 2 + c = 0 Solving 2 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + c = 0 + -2 c = 0 + -2 Combine like terms: 0 + -2 = -2 c = -2 Simplifying c = -2Solution
c = {-4, -2}
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