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Simplifying 0 = 36c + 5c2 + -1c3 Solving 0 = 36c + 5c2 + -1c3 Solving for variable 'c'. Remove the zero: -36c + -5c2 + c3 = 36c + 5c2 + -1c3 + -36c + -5c2 + c3 Reorder the terms: -36c + -5c2 + c3 = 36c + -36c + 5c2 + -5c2 + -1c3 + c3 Combine like terms: 36c + -36c = 0 -36c + -5c2 + c3 = 0 + 5c2 + -5c2 + -1c3 + c3 -36c + -5c2 + c3 = 5c2 + -5c2 + -1c3 + c3 Combine like terms: 5c2 + -5c2 = 0 -36c + -5c2 + c3 = 0 + -1c3 + c3 -36c + -5c2 + c3 = -1c3 + c3 Combine like terms: -1c3 + c3 = 0 -36c + -5c2 + c3 = 0 Factor out the Greatest Common Factor (GCF), 'c'. c(-36 + -5c + c2) = 0 Factor a trinomial. c((-4 + -1c)(9 + -1c)) = 0Subproblem 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 '(-4 + -1c)' equal to zero and attempt to solve: Simplifying -4 + -1c = 0 Solving -4 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1c = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1c = 0 + 4 -1c = 0 + 4 Combine like terms: 0 + 4 = 4 -1c = 4 Divide each side by '-1'. c = -4 Simplifying c = -4Subproblem 3
Set the factor '(9 + -1c)' equal to zero and attempt to solve: Simplifying 9 + -1c = 0 Solving 9 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1c = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1c = 0 + -9 -1c = 0 + -9 Combine like terms: 0 + -9 = -9 -1c = -9 Divide each side by '-1'. c = 9 Simplifying c = 9Solution
c = {0, -4, 9}
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