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Simplifying 6c2 + -78c + 180 = 0 Reorder the terms: 180 + -78c + 6c2 = 0 Solving 180 + -78c + 6c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '6'. 6(30 + -13c + c2) = 0 Factor a trinomial. 6((3 + -1c)(10 + -1c)) = 0 Ignore the factor 6.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 '(10 + -1c)' equal to zero and attempt to solve: Simplifying 10 + -1c = 0 Solving 10 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1c = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1c = 0 + -10 -1c = 0 + -10 Combine like terms: 0 + -10 = -10 -1c = -10 Divide each side by '-1'. c = 10 Simplifying c = 10Solution
c = {3, 10}
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