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Simplifying (3c + 2c)(5 + c) + -1(2c)(5) = 0 Combine like terms: 3c + 2c = 5c (5c)(5 + c) + -1(2c)(5) = 0 Remove parenthesis around (5c) 5c(5 + c) + -1(2c)(5) = 0 (5 * 5c + c * 5c) + -1(2c)(5) = 0 (25c + 5c2) + -1(2c)(5) = 0 Remove parenthesis around (2c) 25c + 5c2 + -1 * 2c(5) = 0 Reorder the terms for easier multiplication: 25c + 5c2 + -1 * 2 * 5c = 0 Multiply -1 * 2 25c + 5c2 + -2 * 5c = 0 Multiply -2 * 5 25c + 5c2 + -10c = 0 Reorder the terms: 25c + -10c + 5c2 = 0 Combine like terms: 25c + -10c = 15c 15c + 5c2 = 0 Solving 15c + 5c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5c'. 5c(3 + c) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve: Simplifying 3 + c = 0 Solving 3 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + c = 0 + -3 c = 0 + -3 Combine like terms: 0 + -3 = -3 c = -3 Simplifying c = -3Solution
c = {0, -3}
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