0=(a-2b+3c)(a+2b-3c)

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Solution for 0=(a-2b+3c)(a+2b-3c) equation: 


Simplifying
0 = (a + -2b + 3c)(a + 2b + -3c)

Multiply (a + -2b + 3c) * (a + 2b + -3c)
0 = (a(a + 2b + -3c) + -2b * (a + 2b + -3c) + 3c * (a + 2b + -3c))
0 = ((a * a + 2b * a + -3c * a) + -2b * (a + 2b + -3c) + 3c * (a + 2b + -3c))

Reorder the terms:
0 = ((2ab + -3ac + a2) + -2b * (a + 2b + -3c) + 3c * (a + 2b + -3c))
0 = ((2ab + -3ac + a2) + -2b * (a + 2b + -3c) + 3c * (a + 2b + -3c))
0 = (2ab + -3ac + a2 + (a * -2b + 2b * -2b + -3c * -2b) + 3c * (a + 2b + -3c))

Reorder the terms:
0 = (2ab + -3ac + a2 + (-2ab + 6bc + -4b2) + 3c * (a + 2b + -3c))
0 = (2ab + -3ac + a2 + (-2ab + 6bc + -4b2) + 3c * (a + 2b + -3c))
0 = (2ab + -3ac + a2 + -2ab + 6bc + -4b2 + (a * 3c + 2b * 3c + -3c * 3c))
0 = (2ab + -3ac + a2 + -2ab + 6bc + -4b2 + (3ac + 6bc + -9c2))

Reorder the terms:
0 = (2ab + -2ab + -3ac + 3ac + a2 + 6bc + 6bc + -4b2 + -9c2)

Combine like terms: 2ab + -2ab = 0
0 = (0 + -3ac + 3ac + a2 + 6bc + 6bc + -4b2 + -9c2)
0 = (-3ac + 3ac + a2 + 6bc + 6bc + -4b2 + -9c2)

Combine like terms: -3ac + 3ac = 0
0 = (0 + a2 + 6bc + 6bc + -4b2 + -9c2)
0 = (a2 + 6bc + 6bc + -4b2 + -9c2)

Combine like terms: 6bc + 6bc = 12bc
0 = (a2 + 12bc + -4b2 + -9c2)

Solving
0 = a2 + 12bc + -4b2 + -9c2

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 + 12bc + -4b2 + -1a2 + -9c2
Remove the zero:
-1a2 = a2 + 12bc + -4b2 + -1a2 + -9c2

Reorder the terms:
-1a2 = a2 + -1a2 + 12bc + -4b2 + -9c2

Combine like terms: a2 + -1a2 = 0
-1a2 = 0 + 12bc + -4b2 + -9c2
-1a2 = 12bc + -4b2 + -9c2

Divide each side by '-1'.
a2 = -12bc + 4b2 + 9c2

Simplifying
a2 = -12bc + 4b2 + 9c2

Reorder the terms:
a2 + 12bc + -4b2 + -9c2 = -12bc + 12bc + 4b2 + -4b2 + 9c2 + -9c2

Combine like terms: -12bc + 12bc = 0
a2 + 12bc + -4b2 + -9c2 = 0 + 4b2 + -4b2 + 9c2 + -9c2
a2 + 12bc + -4b2 + -9c2 = 4b2 + -4b2 + 9c2 + -9c2

Combine like terms: 4b2 + -4b2 = 0
a2 + 12bc + -4b2 + -9c2 = 0 + 9c2 + -9c2
a2 + 12bc + -4b2 + -9c2 = 9c2 + -9c2

Combine like terms: 9c2 + -9c2 = 0
a2 + 12bc + -4b2 + -9c2 = 0

The solution to this equation could not be determined.

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