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Simplifying 48c3 + 84c2 + 30c = 0 Reorder the terms: 30c + 84c2 + 48c3 = 0 Solving 30c + 84c2 + 48c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '6c'. 6c(5 + 14c + 8c2) = 0 Factor a trinomial. 6c((5 + 4c)(1 + 2c)) = 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 '(5 + 4c)' equal to zero and attempt to solve: Simplifying 5 + 4c = 0 Solving 5 + 4c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4c = 0 + -5 4c = 0 + -5 Combine like terms: 0 + -5 = -5 4c = -5 Divide each side by '4'. c = -1.25 Simplifying c = -1.25Subproblem 3
Set the factor '(1 + 2c)' equal to zero and attempt to solve: Simplifying 1 + 2c = 0 Solving 1 + 2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2c = 0 + -1 2c = 0 + -1 Combine like terms: 0 + -1 = -1 2c = -1 Divide each side by '2'. c = -0.5 Simplifying c = -0.5Solution
c = {0, -1.25, -0.5}
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