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Simplifying cx + c2 = 5c2 + -7cx Reorder the terms: cx + c2 = -7cx + 5c2 Solving cx + c2 = -7cx + 5c2 Solving for variable 'c'. Reorder the terms: cx + 7cx + c2 + -5c2 = -7cx + 5c2 + 7cx + -5c2 Combine like terms: cx + 7cx = 8cx 8cx + c2 + -5c2 = -7cx + 5c2 + 7cx + -5c2 Combine like terms: c2 + -5c2 = -4c2 8cx + -4c2 = -7cx + 5c2 + 7cx + -5c2 Reorder the terms: 8cx + -4c2 = -7cx + 7cx + 5c2 + -5c2 Combine like terms: -7cx + 7cx = 0 8cx + -4c2 = 0 + 5c2 + -5c2 8cx + -4c2 = 5c2 + -5c2 Combine like terms: 5c2 + -5c2 = 0 8cx + -4c2 = 0 Factor out the Greatest Common Factor (GCF), '4c'. 4c(2x + -1c) = 0 Ignore the factor 4.Subproblem 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 '(2x + -1c)' equal to zero and attempt to solve: Simplifying 2x + -1c = 0 Reorder the terms: -1c + 2x = 0 Solving -1c + 2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-2x' to each side of the equation. -1c + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 -1c + 0 = 0 + -2x -1c = 0 + -2x Remove the zero: -1c = -2x Divide each side by '-1'. c = 2x Simplifying c = 2xSolution
c = {0, 2x}
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