5ax=c+12a-(c-ax)

Solution for 5ax=c+12a-(c-ax) equation:

Simplifying
5ax = c + 12a + -1(c + -1ax)

Reorder the terms:
5ax = c + 12a + -1(-1ax + c)
5ax = c + 12a + (-1ax * -1 + c * -1)
5ax = c + 12a + (1ax + -1c)

Reorder the terms:
5ax = 12a + 1ax + c + -1c

Combine like terms: c + -1c = 0
5ax = 12a + 1ax + 0
5ax = 12a + 1ax

Solving
5ax = 12a + 1ax

Solving for variable 'a'.

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

Add '-12a' to each side of the equation.
-12a + 5ax = 12a + -12a + 1ax

Combine like terms: 12a + -12a = 0
-12a + 5ax = 0 + 1ax
-12a + 5ax = 1ax

Add '-1ax' to each side of the equation.
-12a + 5ax + -1ax = 1ax + -1ax

Combine like terms: 5ax + -1ax = 4ax
-12a + 4ax = 1ax + -1ax

Combine like terms: 1ax + -1ax = 0
-12a + 4ax = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-3 + x) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Add '-1x' to each side of the equation.
x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
0 = 3 + -1x

Simplifying
0 = 3 + -1x

The solution to this equation could not be determined.

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