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Simplifying 18c4 + 57c3 + -10c2 = 0 Reorder the terms: -10c2 + 57c3 + 18c4 = 0 Solving -10c2 + 57c3 + 18c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c2'. c2(-10 + 57c + 18c2) = 0 Factor a trinomial. c2((-10 + -3c)(1 + -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 '(-10 + -3c)' equal to zero and attempt to solve: Simplifying -10 + -3c = 0 Solving -10 + -3c = 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 + -3c = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3c = 0 + 10 -3c = 0 + 10 Combine like terms: 0 + 10 = 10 -3c = 10 Divide each side by '-3'. c = -3.333333333 Simplifying c = -3.333333333Subproblem 3
Set the factor '(1 + -6c)' equal to zero and attempt to solve: Simplifying 1 + -6c = 0 Solving 1 + -6c = 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 + -6c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6c = 0 + -1 -6c = 0 + -1 Combine like terms: 0 + -1 = -1 -6c = -1 Divide each side by '-6'. c = 0.1666666667 Simplifying c = 0.1666666667Solution
c = {0, -3.333333333, 0.1666666667}
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