xa+By+Cz=D

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Solution for xa+By+Cz=D equation: 


Simplifying
xa + By + Cz = D

Solving
ax + yB + zC = D

Solving for variable 'a'.

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

Add '-1yB' to each side of the equation.
ax + yB + -1yB + zC = D + -1yB

Combine like terms: yB + -1yB = 0
ax + 0 + zC = D + -1yB
ax + zC = D + -1yB

Add '-1zC' to each side of the equation.
ax + zC + -1zC = D + -1yB + -1zC

Combine like terms: zC + -1zC = 0
ax + 0 = D + -1yB + -1zC
ax = D + -1yB + -1zC

Divide each side by 'x'.
a = x-1D + -1x-1yB + -1x-1zC

Simplifying
a = x-1D + -1x-1yB + -1x-1zC

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