(a+b+c)(a-b-c)=a*2-b*2+2bc-c*2

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Solution for (a+b+c)(a-b-c)=a*2-b*2+2bc-c*2 equation: 


Simplifying
(a + b + c)(a + -1b + -1c) = a * 2 + -1b * 2 + 2bc + -1c * 2

Multiply (a + b + c) * (a + -1b + -1c)
(a(a + -1b + -1c) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2
((a * a + -1b * a + -1c * a) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2

Reorder the terms:
((-1ab + -1ac + a2) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2
((-1ab + -1ac + a2) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2
(-1ab + -1ac + a2 + (a * b + -1b * b + -1c * b) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2

Reorder the terms:
(-1ab + -1ac + a2 + (ab + -1bc + -1b2) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2
(-1ab + -1ac + a2 + (ab + -1bc + -1b2) + c(a + -1b + -1c)) = a * 2 + -1b * 2 + 2bc + -1c * 2
(-1ab + -1ac + a2 + ab + -1bc + -1b2 + (a * c + -1b * c + -1c * c)) = a * 2 + -1b * 2 + 2bc + -1c * 2
(-1ab + -1ac + a2 + ab + -1bc + -1b2 + (ac + -1bc + -1c2)) = a * 2 + -1b * 2 + 2bc + -1c * 2

Reorder the terms:
(-1ab + ab + -1ac + ac + a2 + -1bc + -1bc + -1b2 + -1c2) = a * 2 + -1b * 2 + 2bc + -1c * 2

Combine like terms: -1ab + ab = 0
(0 + -1ac + ac + a2 + -1bc + -1bc + -1b2 + -1c2) = a * 2 + -1b * 2 + 2bc + -1c * 2
(-1ac + ac + a2 + -1bc + -1bc + -1b2 + -1c2) = a * 2 + -1b * 2 + 2bc + -1c * 2

Combine like terms: -1ac + ac = 0
(0 + a2 + -1bc + -1bc + -1b2 + -1c2) = a * 2 + -1b * 2 + 2bc + -1c * 2
(a2 + -1bc + -1bc + -1b2 + -1c2) = a * 2 + -1b * 2 + 2bc + -1c * 2

Combine like terms: -1bc + -1bc = -2bc
(a2 + -2bc + -1b2 + -1c2) = a * 2 + -1b * 2 + 2bc + -1c * 2

Reorder the terms for easier multiplication:
a2 + -2bc + -1b2 + -1c2 = 2a + -1b * 2 + 2bc + -1c * 2

Reorder the terms for easier multiplication:
a2 + -2bc + -1b2 + -1c2 = 2a + -1 * 2b + 2bc + -1c * 2

Multiply -1 * 2
a2 + -2bc + -1b2 + -1c2 = 2a + -2b + 2bc + -1c * 2

Reorder the terms for easier multiplication:
a2 + -2bc + -1b2 + -1c2 = 2a + -2b + 2bc + -1 * 2c

Multiply -1 * 2
a2 + -2bc + -1b2 + -1c2 = 2a + -2b + 2bc + -2c

Solving
a2 + -2bc + -1b2 + -1c2 = 2a + -2b + 2bc + -2c

Solving for variable 'a'.

Reorder the terms:
-2a + a2 + 2b + -2bc + -2bc + -1b2 + 2c + -1c2 = 2a + -2b + 2bc + -2c + -2a + 2b + -2bc + 2c

Combine like terms: -2bc + -2bc = -4bc
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 2a + -2b + 2bc + -2c + -2a + 2b + -2bc + 2c

Reorder the terms:
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 2a + -2a + -2b + 2b + 2bc + -2bc + -2c + 2c

Combine like terms: 2a + -2a = 0
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 0 + -2b + 2b + 2bc + -2bc + -2c + 2c
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = -2b + 2b + 2bc + -2bc + -2c + 2c

Combine like terms: -2b + 2b = 0
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 0 + 2bc + -2bc + -2c + 2c
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 2bc + -2bc + -2c + 2c

Combine like terms: 2bc + -2bc = 0
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 0 + -2c + 2c
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = -2c + 2c

Combine like terms: -2c + 2c = 0
-2a + a2 + 2b + -4bc + -1b2 + 2c + -1c2 = 0

The solution to this equation could not be determined.

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