(b*a)+(b*c)=d

Solution for (b*a)+(b*c)=d equation:

Simplifying
(b * a) + (b * c) = d

Multiply b * a
(ab) + (b * c) = d
ab + (b * c) = d

Multiply b * c
ab + (bc) = d
ab + bc = d

Solving
ab + bc = d

Solving for variable 'a'.

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

Add '-1bc' to each side of the equation.
ab + bc + -1bc = -1bc + d

Combine like terms: bc + -1bc = 0
ab + 0 = -1bc + d
ab = -1bc + d

Divide each side by 'b'.
a = -1c + b-1d

Simplifying
a = -1c + b-1d

Reorder the terms:
a = b-1d + -1c