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Simplifying cz + c2 = 5c2 + -3cx Reorder the terms: cz + c2 = -3cx + 5c2 Solving cz + c2 = -3cx + 5c2 Solving for variable 'c'. Reorder the terms: 3cx + cz + c2 + -5c2 = -3cx + 5c2 + 3cx + -5c2 Combine like terms: c2 + -5c2 = -4c2 3cx + cz + -4c2 = -3cx + 5c2 + 3cx + -5c2 Reorder the terms: 3cx + cz + -4c2 = -3cx + 3cx + 5c2 + -5c2 Combine like terms: -3cx + 3cx = 0 3cx + cz + -4c2 = 0 + 5c2 + -5c2 3cx + cz + -4c2 = 5c2 + -5c2 Combine like terms: 5c2 + -5c2 = 0 3cx + cz + -4c2 = 0 Factor out the Greatest Common Factor (GCF), 'c'. c(3x + z + -4c) = 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 '(3x + z + -4c)' equal to zero and attempt to solve: Simplifying 3x + z + -4c = 0 Reorder the terms: -4c + 3x + z = 0 Solving -4c + 3x + z = 0 Move all terms containing c to the left, all other terms to the right. Add '-3x' to each side of the equation. -4c + 3x + -3x + z = 0 + -3x Combine like terms: 3x + -3x = 0 -4c + 0 + z = 0 + -3x -4c + z = 0 + -3x Remove the zero: -4c + z = -3x Add '-1z' to each side of the equation. -4c + z + -1z = -3x + -1z Combine like terms: z + -1z = 0 -4c + 0 = -3x + -1z -4c = -3x + -1z Divide each side by '-4'. c = 0.75x + 0.25z Simplifying c = 0.75x + 0.25zSolution
c = {0, 0.75x + 0.25z}
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