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Simplifying 18c4 + -33c3 + 14c2 = 0 Reorder the terms: 14c2 + -33c3 + 18c4 = 0 Solving 14c2 + -33c3 + 18c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c2'. c2(14 + -33c + 18c2) = 0 Factor a trinomial. c2((2 + -3c)(7 + -6c)) = 0Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve: Simplifying c2 = 0 Solving c2 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c2 = 0 Take the square root of each side: c = {0}Subproblem 2
Set the factor '(2 + -3c)' equal to zero and attempt to solve: Simplifying 2 + -3c = 0 Solving 2 + -3c = 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 + -3c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3c = 0 + -2 -3c = 0 + -2 Combine like terms: 0 + -2 = -2 -3c = -2 Divide each side by '-3'. c = 0.6666666667 Simplifying c = 0.6666666667Subproblem 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, 0.6666666667, 1.166666667}
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