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Simplifying 3C2 + -17C + 30 = -24 + 10C Reorder the terms: 30 + -17C + 3C2 = -24 + 10C Solving 30 + -17C + 3C2 = -24 + 10C Solving for variable 'C'. Reorder the terms: 30 + 24 + -17C + -10C + 3C2 = -24 + 10C + 24 + -10C Combine like terms: 30 + 24 = 54 54 + -17C + -10C + 3C2 = -24 + 10C + 24 + -10C Combine like terms: -17C + -10C = -27C 54 + -27C + 3C2 = -24 + 10C + 24 + -10C Reorder the terms: 54 + -27C + 3C2 = -24 + 24 + 10C + -10C Combine like terms: -24 + 24 = 0 54 + -27C + 3C2 = 0 + 10C + -10C 54 + -27C + 3C2 = 10C + -10C Combine like terms: 10C + -10C = 0 54 + -27C + 3C2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(18 + -9C + C2) = 0 Factor a trinomial. 3((3 + -1C)(6 + -1C)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1C)' equal to zero and attempt to solve: Simplifying 3 + -1C = 0 Solving 3 + -1C = 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 + -1C = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1C = 0 + -3 -1C = 0 + -3 Combine like terms: 0 + -3 = -3 -1C = -3 Divide each side by '-1'. C = 3 Simplifying C = 3Subproblem 2
Set the factor '(6 + -1C)' equal to zero and attempt to solve: Simplifying 6 + -1C = 0 Solving 6 + -1C = 0 Move all terms containing C to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1C = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1C = 0 + -6 -1C = 0 + -6 Combine like terms: 0 + -6 = -6 -1C = -6 Divide each side by '-1'. C = 6 Simplifying C = 6Solution
C = {3, 6}
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