(a+b+c)(a+b+c)-(a+b-c)(a+b-c)=

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


Simplifying
(a + b + c)(a + b + c) + -1(a + b + -1c)(a + b + -1c) = 0

Multiply (a + b + c) * (a + b + c)
(a(a + b + c) + b(a + b + c) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0
((a * a + b * a + c * a) + b(a + b + c) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0

Reorder the terms:
((ab + ac + a2) + b(a + b + c) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0
((ab + ac + a2) + b(a + b + c) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0
(ab + ac + a2 + (a * b + b * b + c * b) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0

Reorder the terms:
(ab + ac + a2 + (ab + bc + b2) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0
(ab + ac + a2 + (ab + bc + b2) + c(a + b + c)) + -1(a + b + -1c)(a + b + -1c) = 0
(ab + ac + a2 + ab + bc + b2 + (a * c + b * c + c * c)) + -1(a + b + -1c)(a + b + -1c) = 0
(ab + ac + a2 + ab + bc + b2 + (ac + bc + c2)) + -1(a + b + -1c)(a + b + -1c) = 0

Reorder the terms:
(ab + ab + ac + ac + a2 + bc + bc + b2 + c2) + -1(a + b + -1c)(a + b + -1c) = 0

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

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

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

Multiply (a + b + -1c) * (a + b + -1c)
2ab + 2ac + a2 + 2bc + b2 + c2 + -1(a(a + b + -1c) + b(a + b + -1c) + -1c * (a + b + -1c)) = 0
2ab + 2ac + a2 + 2bc + b2 + c2 + -1((a * a + b * a + -1c * a) + b(a + b + -1c) + -1c * (a + b + -1c)) = 0

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

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

Reorder the terms:
2ab + 2ac + a2 + 2bc + b2 + c2 + -1(ab + ab + -1ac + -1ac + a2 + -1bc + -1bc + b2 + 1c2) = 0

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

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

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

Reorder the terms:
2ab + -2ab + 2ac + 2ac + a2 + -1a2 + 2bc + 2bc + b2 + -1b2 + c2 + -1c2 = 0

Combine like terms: 2ab + -2ab = 0
0 + 2ac + 2ac + a2 + -1a2 + 2bc + 2bc + b2 + -1b2 + c2 + -1c2 = 0
2ac + 2ac + a2 + -1a2 + 2bc + 2bc + b2 + -1b2 + c2 + -1c2 = 0

Combine like terms: 2ac + 2ac = 4ac
4ac + a2 + -1a2 + 2bc + 2bc + b2 + -1b2 + c2 + -1c2 = 0

Combine like terms: a2 + -1a2 = 0
4ac + 0 + 2bc + 2bc + b2 + -1b2 + c2 + -1c2 = 0
4ac + 2bc + 2bc + b2 + -1b2 + c2 + -1c2 = 0

Combine like terms: 2bc + 2bc = 4bc
4ac + 4bc + b2 + -1b2 + c2 + -1c2 = 0

Combine like terms: b2 + -1b2 = 0
4ac + 4bc + 0 + c2 + -1c2 = 0
4ac + 4bc + c2 + -1c2 = 0

Combine like terms: c2 + -1c2 = 0
4ac + 4bc + 0 = 0
4ac + 4bc = 0

Solving
4ac + 4bc = 0

Solving for variable 'a'.

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

Add '-4bc' to each side of the equation.
4ac + 4bc + -4bc = 0 + -4bc

Combine like terms: 4bc + -4bc = 0
4ac + 0 = 0 + -4bc
4ac = 0 + -4bc
Remove the zero:
4ac = -4bc

Divide each side by '4c'.
a = -1b

Simplifying
a = -1b

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