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

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

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

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

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

Multiply (-1 + x) * (2 + x2)
(-1(2 + x2) + x(2 + x2)) = (x + -3)(x2 + 1)
((2 * -1 + x2 * -1) + x(2 + x2)) = (x + -3)(x2 + 1)
((-2 + -1x2) + x(2 + x2)) = (x + -3)(x2 + 1)
(-2 + -1x2 + (2 * x + x2 * x)) = (x + -3)(x2 + 1)
(-2 + -1x2 + (2x + x3)) = (x + -3)(x2 + 1)

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

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

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

Multiply (-3 + x) * (1 + x2)
-2 + 2x + -1x2 + x3 = (-3(1 + x2) + x(1 + x2))
-2 + 2x + -1x2 + x3 = ((1 * -3 + x2 * -3) + x(1 + x2))
-2 + 2x + -1x2 + x3 = ((-3 + -3x2) + x(1 + x2))
-2 + 2x + -1x2 + x3 = (-3 + -3x2 + (1 * x + x2 * x))
-2 + 2x + -1x2 + x3 = (-3 + -3x2 + (1x + x3))

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

Add '-1x3' to each side of the equation.
-2 + 2x + -1x2 + x3 + -1x3 = -3 + 1x + -3x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-2 + 2x + -1x2 + 0 = -3 + 1x + -3x2 + x3 + -1x3
-2 + 2x + -1x2 = -3 + 1x + -3x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-2 + 2x + -1x2 = -3 + 1x + -3x2 + 0
-2 + 2x + -1x2 = -3 + 1x + -3x2

Solving
-2 + 2x + -1x2 = -3 + 1x + -3x2

Solving for variable 'x'.

Reorder the terms:
-2 + 3 + 2x + -1x + -1x2 + 3x2 = -3 + 1x + -3x2 + 3 + -1x + 3x2

Combine like terms: -2 + 3 = 1
1 + 2x + -1x + -1x2 + 3x2 = -3 + 1x + -3x2 + 3 + -1x + 3x2

Combine like terms: 2x + -1x = 1x
1 + 1x + -1x2 + 3x2 = -3 + 1x + -3x2 + 3 + -1x + 3x2

Combine like terms: -1x2 + 3x2 = 2x2
1 + 1x + 2x2 = -3 + 1x + -3x2 + 3 + -1x + 3x2

Reorder the terms:
1 + 1x + 2x2 = -3 + 3 + 1x + -1x + -3x2 + 3x2

Combine like terms: -3 + 3 = 0
1 + 1x + 2x2 = 0 + 1x + -1x + -3x2 + 3x2
1 + 1x + 2x2 = 1x + -1x + -3x2 + 3x2

Combine like terms: 1x + -1x = 0
1 + 1x + 2x2 = 0 + -3x2 + 3x2
1 + 1x + 2x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
1 + 1x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.5x + x2 = 0 + -0.5
0.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.5x + x2 = -0.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.5 + 0.0625

Combine like terms: -0.5 + 0.0625 = -0.4375
0.0625 + 0.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -0.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.