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

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

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

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

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

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

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

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

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

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

Solving
a2 + 2bc + -1b2 + -1c2 = 0

Solving for variable 'a'.

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

Add '-2bc' to each side of the equation.
a2 + 2bc + -1b2 + -2bc + -1c2 = 0 + -2bc

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

Combine like terms: 2bc + -2bc = 0
a2 + 0 + -1b2 + -1c2 = 0 + -2bc
a2 + -1b2 + -1c2 = 0 + -2bc
Remove the zero:
a2 + -1b2 + -1c2 = -2bc

Add 'b2' to each side of the equation.
a2 + -1b2 + b2 + -1c2 = -2bc + b2

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

Add 'c2' to each side of the equation.
a2 + -1c2 + c2 = -2bc + b2 + c2

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

Simplifying
a2 = -2bc + b2 + c2

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

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

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

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

The solution to this equation could not be determined.