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Simplifying 30c3 + 145c2 + -210c = 0 Reorder the terms: -210c + 145c2 + 30c3 = 0 Solving -210c + 145c2 + 30c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5c'. 5c(-42 + 29c + 6c2) = 0 Factor a trinomial. 5c((-6 + -1c)(7 + -6c)) = 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 '(-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 = -6Subproblem 3
Set the factor '(7 + -6c)' equal to zero and attempt to solve: Simplifying 7 + -6c = 0 Solving 7 + -6c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6c = 0 + -7 -6c = 0 + -7 Combine like terms: 0 + -7 = -7 -6c = -7 Divide each side by '-6'. c = 1.166666667 Simplifying c = 1.166666667Solution
c = {0, -6, 1.166666667}
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