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

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


Simplifying
0 = x3 + (2a + 1) * x2 + (a2 + 2a + -1) * x + (a2 + -1)

Reorder the terms:
0 = x3 + (1 + 2a) * x2 + (a2 + 2a + -1) * x + (a2 + -1)

Reorder the terms for easier multiplication:
0 = x3 + x2(1 + 2a) + (a2 + 2a + -1) * x + (a2 + -1)
0 = x3 + (1 * x2 + 2a * x2) + (a2 + 2a + -1) * x + (a2 + -1)

Reorder the terms:
0 = x3 + (2ax2 + 1x2) + (a2 + 2a + -1) * x + (a2 + -1)
0 = x3 + (2ax2 + 1x2) + (a2 + 2a + -1) * x + (a2 + -1)

Reorder the terms:
0 = x3 + 2ax2 + 1x2 + (-1 + 2a + a2) * x + (a2 + -1)

Reorder the terms for easier multiplication:
0 = x3 + 2ax2 + 1x2 + x(-1 + 2a + a2) + (a2 + -1)
0 = x3 + 2ax2 + 1x2 + (-1 * x + 2a * x + a2 * x) + (a2 + -1)

Reorder the terms:
0 = x3 + 2ax2 + 1x2 + (2ax + a2x + -1x) + (a2 + -1)
0 = x3 + 2ax2 + 1x2 + (2ax + a2x + -1x) + (a2 + -1)

Reorder the terms:
0 = x3 + 2ax2 + 1x2 + 2ax + a2x + -1x + (-1 + a2)

Remove parenthesis around (-1 + a2)
0 = x3 + 2ax2 + 1x2 + 2ax + a2x + -1x + -1 + a2

Reorder the terms:
0 = -1 + 2ax + 2ax2 + a2 + a2x + -1x + 1x2 + x3

Solving
0 = -1 + 2ax + 2ax2 + a2 + a2x + -1x + 1x2 + x3

Solving for variable 'a'.

Combine like terms: 0 + 1 = 1
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = -1 + 2ax + 2ax2 + a2 + a2x + -1x + 1x2 + x3 + 1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3

Reorder the terms:
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = -1 + 1 + 2ax + -2ax + 2ax2 + -2ax2 + a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3

Combine like terms: -1 + 1 = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + 2ax + -2ax + 2ax2 + -2ax2 + a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 2ax + -2ax + 2ax2 + -2ax2 + a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3

Combine like terms: 2ax + -2ax = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + 2ax2 + -2ax2 + a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 2ax2 + -2ax2 + a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3

Combine like terms: 2ax2 + -2ax2 = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = a2 + -1a2 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3

Combine like terms: a2 + -1a2 = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = a2x + -1a2x + -1x + x + 1x2 + -1x2 + x3 + -1x3

Combine like terms: a2x + -1a2x = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + -1x + x + 1x2 + -1x2 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = -1x + x + 1x2 + -1x2 + x3 + -1x3

Combine like terms: -1x + x = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + 1x2 + -1x2 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 1x2 + -1x2 + x3 + -1x3

Combine like terms: 1x2 + -1x2 = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0 + x3 + -1x3
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
1 + -2ax + -2ax2 + -1a2 + -1a2x + x + -1x2 + -1x3 = 0

The solution to this equation could not be determined.

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