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

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


Simplifying
0 = (a + -2b + c)(a + 2b + -1c)

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

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

Reorder the terms:
0 = (2ab + -1ac + a2 + (-2ab + 2bc + -4b2) + c(a + 2b + -1c))
0 = (2ab + -1ac + a2 + (-2ab + 2bc + -4b2) + c(a + 2b + -1c))
0 = (2ab + -1ac + a2 + -2ab + 2bc + -4b2 + (a * c + 2b * c + -1c * c))
0 = (2ab + -1ac + a2 + -2ab + 2bc + -4b2 + (ac + 2bc + -1c2))

Reorder the terms:
0 = (2ab + -2ab + -1ac + ac + a2 + 2bc + 2bc + -4b2 + -1c2)

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

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

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

Solving
0 = a2 + 4bc + -4b2 + -1c2

Solving for variable 'a'.

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

Add '-1a2' to each side of the equation.
0 + -1a2 = a2 + 4bc + -4b2 + -1a2 + -1c2
Remove the zero:
-1a2 = a2 + 4bc + -4b2 + -1a2 + -1c2

Reorder the terms:
-1a2 = a2 + -1a2 + 4bc + -4b2 + -1c2

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

Divide each side by '-1'.
a2 = -4bc + 4b2 + c2

Simplifying
a2 = -4bc + 4b2 + c2

Reorder the terms:
a2 + 4bc + -4b2 + -1c2 = -4bc + 4bc + 4b2 + -4b2 + c2 + -1c2

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

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

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

The solution to this equation could not be determined.

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