cx+c(2)=5c(2)-7cx

Solution for cx+c(2)=5c(2)-7cx equation:

Simplifying
cx + c(2) = 5c(2) + -7cx

Reorder the terms for easier multiplication:
cx + 2c = 5c(2) + -7cx

Reorder the terms:
2c + cx = 5c(2) + -7cx

Reorder the terms for easier multiplication:
2c + cx = 5 * 2c + -7cx

Multiply 5 * 2
2c + cx = 10c + -7cx

Solving
2c + cx = 10c + -7cx

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-10c' to each side of the equation.
2c + -10c + cx = 10c + -10c + -7cx

Combine like terms: 2c + -10c = -8c
-8c + cx = 10c + -10c + -7cx

Combine like terms: 10c + -10c = 0
-8c + cx = 0 + -7cx
-8c + cx = -7cx

Add '7cx' to each side of the equation.
-8c + cx + 7cx = -7cx + 7cx

Combine like terms: cx + 7cx = 8cx
-8c + 8cx = -7cx + 7cx

Combine like terms: -7cx + 7cx = 0
-8c + 8cx = 0

Factor out the Greatest Common Factor (GCF), '8c'.
8c(-1 + x) = 0

Ignore the factor 8.
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 = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Add '-1x' to each side of the equation.
x + -1x = 1 + -1x

Combine like terms: x + -1x = 0
0 = 1 + -1x

Simplifying
0 = 1 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
c = {0}