C^4-24C^3+144C^2=0

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Solution for C^4-24C^3+144C^2=0 equation:


Simplifying
C4 + -24C3 + 144C2 = 0

Reorder the terms:
144C2 + -24C3 + C4 = 0

Solving
144C2 + -24C3 + C4 = 0

Solving for variable 'C'.

Factor out the Greatest Common Factor (GCF), 'C2'.
C2(144 + -24C + C2) = 0

Factor a trinomial.
C2((12 + -1C)(12 + -1C)) = 0

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 '(12 + -1C)' equal to zero and attempt to solve: Simplifying 12 + -1C = 0 Solving 12 + -1C = 0 Move all terms containing C to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1C = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1C = 0 + -12 -1C = 0 + -12 Combine like terms: 0 + -12 = -12 -1C = -12 Divide each side by '-1'. C = 12 Simplifying C = 12

Subproblem 3

Set the factor '(12 + -1C)' equal to zero and attempt to solve: Simplifying 12 + -1C = 0 Solving 12 + -1C = 0 Move all terms containing C to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1C = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1C = 0 + -12 -1C = 0 + -12 Combine like terms: 0 + -12 = -12 -1C = -12 Divide each side by '-1'. C = 12 Simplifying C = 12

Solution

C = {0, 12, 12}

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