ab+c(d-e)=f-10

Solution for ab+c(d-e)=f-10 equation:

Simplifying
ab + c(d + -1e) = f + -10
ab + (d * c + -1e * c) = f + -10
ab + (cd + -1ce) = f + -10

Reorder the terms:
ab + cd + -1ce = -10 + f

Solving
ab + cd + -1ce = -10 + f

Solving for variable 'a'.

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

Add '-1cd' to each side of the equation.
ab + cd + -1cd + -1ce = -10 + -1cd + f

Combine like terms: cd + -1cd = 0
ab + 0 + -1ce = -10 + -1cd + f
ab + -1ce = -10 + -1cd + f

Add 'ce' to each side of the equation.
ab + -1ce + ce = -10 + -1cd + ce + f

Combine like terms: -1ce + ce = 0
ab + 0 = -10 + -1cd + ce + f
ab = -10 + -1cd + ce + f

Divide each side by 'b'.
a = -10b-1 + -1b-1cd + b-1ce + b-1f

Simplifying
a = -10b-1 + -1b-1cd + b-1ce + b-1f