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Simplifying 20c4 + -32c3 + -16c2 = 0 Reorder the terms: -16c2 + -32c3 + 20c4 = 0 Solving -16c2 + -32c3 + 20c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4c2'. 4c2(-4 + -8c + 5c2) = 0 Factor a trinomial. 4c2((-2 + -5c)(2 + -1c)) = 0 Ignore the factor 4.Subproblem 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 + -5c)' equal to zero and attempt to solve: Simplifying -2 + -5c = 0 Solving -2 + -5c = 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 + -5c = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5c = 0 + 2 -5c = 0 + 2 Combine like terms: 0 + 2 = 2 -5c = 2 Divide each side by '-5'. c = -0.4 Simplifying c = -0.4Subproblem 3
Set the factor '(2 + -1c)' equal to zero and attempt to solve: Simplifying 2 + -1c = 0 Solving 2 + -1c = 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 + -1c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1c = 0 + -2 -1c = 0 + -2 Combine like terms: 0 + -2 = -2 -1c = -2 Divide each side by '-1'. c = 2 Simplifying c = 2Solution
c = {0, -0.4, 2}
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