G(f-a-b)=g(F-A-(1000-b))

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Solution for G(f-a-b)=g(F-A-(1000-b)) equation: 


Simplifying
G(f + -1a + -1b) = g(F + -1A + -1(1000 + -1b))

Reorder the terms:
G(-1a + -1b + f) = g(F + -1A + -1(1000 + -1b))
(-1a * G + -1b * G + f * G) = g(F + -1A + -1(1000 + -1b))
(-1aG + -1bG + fG) = g(F + -1A + -1(1000 + -1b))
-1aG + -1bG + fG = g(F + -1A + (1000 * -1 + -1b * -1))
-1aG + -1bG + fG = g(F + -1A + (-1000 + 1b))

Reorder the terms:
-1aG + -1bG + fG = g(-1000 + -1A + F + 1b)
-1aG + -1bG + fG = (-1000 * g + -1A * g + F * g + 1b * g)

Reorder the terms:
-1aG + -1bG + fG = (1bg + -1000g + -1gA + gF)
-1aG + -1bG + fG = (1bg + -1000g + -1gA + gF)

Solving
-1aG + -1bG + fG = 1bg + -1000g + -1gA + gF

Solving for variable 'a'.

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

Add 'bG' to each side of the equation.
-1aG + -1bG + bG + fG = 1bg + -1000g + -1gA + bG + gF

Combine like terms: -1bG + bG = 0
-1aG + 0 + fG = 1bg + -1000g + -1gA + bG + gF
-1aG + fG = 1bg + -1000g + -1gA + bG + gF

Reorder the terms:
-1aG + fG = bG + 1bg + -1000g + -1gA + gF

Add '-1fG' to each side of the equation.
-1aG + fG + -1fG = bG + 1bg + -1000g + -1gA + -1fG + gF

Combine like terms: fG + -1fG = 0
-1aG + 0 = bG + 1bg + -1000g + -1gA + -1fG + gF
-1aG = bG + 1bg + -1000g + -1gA + -1fG + gF

Reorder the terms:
-1aG = bG + 1bg + -1fG + -1000g + -1gA + gF

Divide each side by '-1G'.
a = -1b + -1bgG-1 + f + 1000gG-1 + gAG-1 + -1gFG-1

Simplifying
a = -1b + -1bgG-1 + f + 1000gG-1 + gAG-1 + -1gFG-1

Reorder the terms:
a = -1b + -1bgG-1 + f + gAG-1 + -1gFG-1 + 1000gG-1

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