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Simplifying 2cx + 8c = 4cx(x + -3) Reorder the terms: 8c + 2cx = 4cx(x + -3) Reorder the terms: 8c + 2cx = 4cx(-3 + x) 8c + 2cx = (-3 * 4cx + x * 4cx) 8c + 2cx = (-12cx + 4cx2) Solving 8c + 2cx = -12cx + 4cx2 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '12cx' to each side of the equation. 8c + 2cx + 12cx = -12cx + 12cx + 4cx2 Combine like terms: 2cx + 12cx = 14cx 8c + 14cx = -12cx + 12cx + 4cx2 Combine like terms: -12cx + 12cx = 0 8c + 14cx = 0 + 4cx2 8c + 14cx = 4cx2 Add '-4cx2' to each side of the equation. 8c + 14cx + -4cx2 = 4cx2 + -4cx2 Combine like terms: 4cx2 + -4cx2 = 0 8c + 14cx + -4cx2 = 0 Factor out the Greatest Common Factor (GCF), '2c'. 2c(4 + 7x + -2x2) = 0 Factor a trinomial. 2c((4 + -1x)(1 + 2x)) = 0 Ignore the factor 2.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
c = {0}
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