a^4-2a^3+a^2-1=(a^2-a-1)(a^2-a+1)

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Solution for a^4-2a^3+a^2-1=(a^2-a-1)(a^2-a+1) equation: 


Simplifying
a4 + -2a3 + a2 + -1 = (a2 + -1a + -1)(a2 + -1a + 1)

Reorder the terms:
-1 + a2 + -2a3 + a4 = (a2 + -1a + -1)(a2 + -1a + 1)

Reorder the terms:
-1 + a2 + -2a3 + a4 = (-1 + -1a + a2)(a2 + -1a + 1)

Reorder the terms:
-1 + a2 + -2a3 + a4 = (-1 + -1a + a2)(1 + -1a + a2)

Multiply (-1 + -1a + a2) * (1 + -1a + a2)
-1 + a2 + -2a3 + a4 = (-1(1 + -1a + a2) + -1a * (1 + -1a + a2) + a2(1 + -1a + a2))
-1 + a2 + -2a3 + a4 = ((1 * -1 + -1a * -1 + a2 * -1) + -1a * (1 + -1a + a2) + a2(1 + -1a + a2))
-1 + a2 + -2a3 + a4 = ((-1 + 1a + -1a2) + -1a * (1 + -1a + a2) + a2(1 + -1a + a2))
-1 + a2 + -2a3 + a4 = (-1 + 1a + -1a2 + (1 * -1a + -1a * -1a + a2 * -1a) + a2(1 + -1a + a2))
-1 + a2 + -2a3 + a4 = (-1 + 1a + -1a2 + (-1a + 1a2 + -1a3) + a2(1 + -1a + a2))
-1 + a2 + -2a3 + a4 = (-1 + 1a + -1a2 + -1a + 1a2 + -1a3 + (1 * a2 + -1a * a2 + a2 * a2))
-1 + a2 + -2a3 + a4 = (-1 + 1a + -1a2 + -1a + 1a2 + -1a3 + (1a2 + -1a3 + a4))

Reorder the terms:
-1 + a2 + -2a3 + a4 = (-1 + 1a + -1a + -1a2 + 1a2 + 1a2 + -1a3 + -1a3 + a4)

Combine like terms: 1a + -1a = 0
-1 + a2 + -2a3 + a4 = (-1 + 0 + -1a2 + 1a2 + 1a2 + -1a3 + -1a3 + a4)
-1 + a2 + -2a3 + a4 = (-1 + -1a2 + 1a2 + 1a2 + -1a3 + -1a3 + a4)

Combine like terms: -1a2 + 1a2 = 0
-1 + a2 + -2a3 + a4 = (-1 + 0 + 1a2 + -1a3 + -1a3 + a4)
-1 + a2 + -2a3 + a4 = (-1 + 1a2 + -1a3 + -1a3 + a4)

Combine like terms: -1a3 + -1a3 = -2a3
-1 + a2 + -2a3 + a4 = (-1 + 1a2 + -2a3 + a4)

Add '1' to each side of the equation.
-1 + a2 + -2a3 + 1 + a4 = -1 + 1a2 + -2a3 + 1 + a4

Reorder the terms:
-1 + 1 + a2 + -2a3 + a4 = -1 + 1a2 + -2a3 + 1 + a4

Combine like terms: -1 + 1 = 0
0 + a2 + -2a3 + a4 = -1 + 1a2 + -2a3 + 1 + a4
a2 + -2a3 + a4 = -1 + 1a2 + -2a3 + 1 + a4

Reorder the terms:
a2 + -2a3 + a4 = -1 + 1 + 1a2 + -2a3 + a4

Combine like terms: -1 + 1 = 0
a2 + -2a3 + a4 = 0 + 1a2 + -2a3 + a4
a2 + -2a3 + a4 = 1a2 + -2a3 + a4

Add '2a3' to each side of the equation.
a2 + -2a3 + 2a3 + a4 = 1a2 + -2a3 + 2a3 + a4

Combine like terms: -2a3 + 2a3 = 0
a2 + 0 + a4 = 1a2 + -2a3 + 2a3 + a4
a2 + a4 = 1a2 + -2a3 + 2a3 + a4

Combine like terms: -2a3 + 2a3 = 0
a2 + a4 = 1a2 + 0 + a4
a2 + a4 = 1a2 + a4

Add '-1a4' to each side of the equation.
a2 + a4 + -1a4 = 1a2 + a4 + -1a4

Combine like terms: a4 + -1a4 = 0
a2 + 0 = 1a2 + a4 + -1a4
a2 = 1a2 + a4 + -1a4

Combine like terms: a4 + -1a4 = 0
a2 = 1a2 + 0
a2 = 1a2

Solving
a2 = 1a2

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.
a2 + -1a2 = 1a2 + -1a2

Combine like terms: a2 + -1a2 = 0
0 = 1a2 + -1a2

Combine like terms: 1a2 + -1a2 = 0
0 = 0

Simplifying
0 = 0

The solution to this equation could not be determined.

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