ab-bc-bd+be-bg=0

Solution for ab-bc-bd+be-bg=0 equation:

Simplifying
ab + -1bc + -1bd + be + -1bg = 0

Solving
ab + -1bc + -1bd + be + -1bg = 0

Solving for variable 'a'.

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

Add 'bc' to each side of the equation.
ab + -1bc + -1bd + be + bc + -1bg = 0 + bc

Reorder the terms:
ab + -1bc + bc + -1bd + be + -1bg = 0 + bc

Combine like terms: -1bc + bc = 0
ab + 0 + -1bd + be + -1bg = 0 + bc
ab + -1bd + be + -1bg = 0 + bc
Remove the zero:
ab + -1bd + be + -1bg = bc

Add 'bd' to each side of the equation.
ab + -1bd + be + bd + -1bg = bc + bd

Reorder the terms:
ab + -1bd + bd + be + -1bg = bc + bd

Combine like terms: -1bd + bd = 0
ab + 0 + be + -1bg = bc + bd
ab + be + -1bg = bc + bd

Add '-1be' to each side of the equation.
ab + be + -1be + -1bg = bc + bd + -1be

Combine like terms: be + -1be = 0
ab + 0 + -1bg = bc + bd + -1be
ab + -1bg = bc + bd + -1be

Add 'bg' to each side of the equation.
ab + -1bg + bg = bc + bd + -1be + bg

Combine like terms: -1bg + bg = 0
ab + 0 = bc + bd + -1be + bg
ab = bc + bd + -1be + bg

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

Simplifying
a = c + d + -1e + g