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Simplifying 5c4 + -5c2 + -60 = 0 Reorder the terms: -60 + -5c2 + 5c4 = 0 Solving -60 + -5c2 + 5c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5'. 5(-12 + -1c2 + c4) = 0 Factor a trinomial. 5((-3 + -1c2)(4 + -1c2)) = 0 Factor a difference between two squares. 5((-3 + -1c2)((2 + c)(2 + -1c))) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1c2)' equal to zero and attempt to solve: Simplifying -3 + -1c2 = 0 Solving -3 + -1c2 = 0 Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1c2 = 0 + 3 -1c2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1c2 = 3 Divide each side by '-1'. c2 = -3 Simplifying c2 = -3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + c)' equal to zero and attempt to solve: Simplifying 2 + c = 0 Solving 2 + c = 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 + c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + c = 0 + -2 c = 0 + -2 Combine like terms: 0 + -2 = -2 c = -2 Simplifying c = -2Subproblem 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 = {-2, 2}
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