(x^2+2)*(sqrt(x^2-x+1))=x^3+2x^2-3x+1

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


Simplifying
(x2 + 2)(sqrt(x2 + -1x + 1)) = x3 + 2x2 + -3x + 1

Reorder the terms:
(2 + x2)(sqrt(x2 + -1x + 1)) = x3 + 2x2 + -3x + 1

Reorder the terms:
(2 + x2)(qrst(1 + -1x + x2)) = x3 + 2x2 + -3x + 1
(2 + x2)((1 * qrst + -1x * qrst + x2 * qrst)) = x3 + 2x2 + -3x + 1
(2 + x2)((1qrst + -1qrstx + qrstx2)) = x3 + 2x2 + -3x + 1

Multiply (2 + x2) * (1qrst + -1qrstx + qrstx2)
(2(1qrst + -1qrstx + qrstx2) + x2(1qrst + -1qrstx + qrstx2)) = x3 + 2x2 + -3x + 1
((1qrst * 2 + -1qrstx * 2 + qrstx2 * 2) + x2(1qrst + -1qrstx + qrstx2)) = x3 + 2x2 + -3x + 1
((2qrst + -2qrstx + 2qrstx2) + x2(1qrst + -1qrstx + qrstx2)) = x3 + 2x2 + -3x + 1
(2qrst + -2qrstx + 2qrstx2 + (1qrst * x2 + -1qrstx * x2 + qrstx2 * x2)) = x3 + 2x2 + -3x + 1
(2qrst + -2qrstx + 2qrstx2 + (1qrstx2 + -1qrstx3 + qrstx4)) = x3 + 2x2 + -3x + 1

Combine like terms: 2qrstx2 + 1qrstx2 = 3qrstx2
(2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4) = x3 + 2x2 + -3x + 1

Reorder the terms:
2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 = 1 + -3x + 2x2 + x3

Solving
2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 = 1 + -3x + 2x2 + x3

Solving for variable 'q'.

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

Reorder the terms:
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 1 + -3x + 2x2 + x3 + -1 + 3x + -2x2 + -1x3

Reorder the terms:
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 1 + -1 + -3x + 3x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: 1 + -1 = 0
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 0 + -3x + 3x + 2x2 + -2x2 + x3 + -1x3
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = -3x + 3x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -3x + 3x = 0
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3

Combine like terms: 2x2 + -2x2 = 0
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 0 + x3 + -1x3
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-1 + 2qrst + -2qrstx + 3qrstx2 + -1qrstx3 + qrstx4 + 3x + -2x2 + -1x3 = 0

The solution to this equation could not be determined.

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