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Simplifying 12c2 + (15c2 + 30c) = (21c2 + 42c) Reorder the terms: 12c2 + (30c + 15c2) = (21c2 + 42c) Remove parenthesis around (30c + 15c2) 12c2 + 30c + 15c2 = (21c2 + 42c) Reorder the terms: 30c + 12c2 + 15c2 = (21c2 + 42c) Combine like terms: 12c2 + 15c2 = 27c2 30c + 27c2 = (21c2 + 42c) Reorder the terms: 30c + 27c2 = (42c + 21c2) Remove parenthesis around (42c + 21c2) 30c + 27c2 = 42c + 21c2 Solving 30c + 27c2 = 42c + 21c2 Solving for variable 'c'. Reorder the terms: 30c + -42c + 27c2 + -21c2 = 42c + 21c2 + -42c + -21c2 Combine like terms: 30c + -42c = -12c -12c + 27c2 + -21c2 = 42c + 21c2 + -42c + -21c2 Combine like terms: 27c2 + -21c2 = 6c2 -12c + 6c2 = 42c + 21c2 + -42c + -21c2 Reorder the terms: -12c + 6c2 = 42c + -42c + 21c2 + -21c2 Combine like terms: 42c + -42c = 0 -12c + 6c2 = 0 + 21c2 + -21c2 -12c + 6c2 = 21c2 + -21c2 Combine like terms: 21c2 + -21c2 = 0 -12c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '6c'. 6c(-2 + c) = 0 Ignore the factor 6.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 '(-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 = {0, 2}
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