By using simple algebra, we will see that the solution of the given equation is:
x = (a - c + ab)/(a + b)
How to solve the equation?
Here we have the equation:
a*(x - b) + bx + c = a
And we want to solve it for x.
First, we need to move all the terms with x to the left side and all the others to the right side:
a*x - a*b + b*x + c = a
x*(a + b) - ab + c = a
x*(a + b) = a - c + ab
Now we divide both sides by a + b
x = (a - c + ab)/(a + b)
Now the restriction of a ≠ -b comes useful because this implies that the denominator is never equal to zero.
If you want to learn more about algebra, you can read:
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