a(bx+c)=c(a+ab)

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Solution for a(bx+c)=c(a+ab) equation: 


Simplifying
a(bx + c) = c(a + ab)
(bx * a + c * a) = c(a + ab)
(abx + ac) = c(a + ab)
abx + ac = (a * c + ab * c)

Reorder the terms:
abx + ac = (abc + ac)
abx + ac = (abc + ac)

Add '-1ac' to each side of the equation.
abx + ac + -1ac = abc + ac + -1ac

Combine like terms: ac + -1ac = 0
abx + 0 = abc + ac + -1ac
abx = abc + ac + -1ac

Combine like terms: ac + -1ac = 0
abx = abc + 0
abx = abc

Solving
abx = abc

Solving for variable 'a'.

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

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

Combine like terms: abc + -1abc = 0
-1abc + abx = 0

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


Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve:

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1c + x)' equal to zero and attempt to solve:

Simplifying
-1c + x = 0

Solving
-1c + x = 0

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

Add 'c' to each side of the equation.
-1c + c + x = 0 + c

Combine like terms: -1c + c = 0
0 + x = 0 + c
x = 0 + c
Remove the zero:
x = c

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

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

Simplifying
0 = c + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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