5x^3-2x^2+3x+1=1

Solution for 5x^3-2x^2+3x+1=1 equation:

Simplifying
5x3 + -2x2 + 3x + 1 = 1

Reorder the terms:
1 + 3x + -2x2 + 5x3 = 1

Add '-1' to each side of the equation.
1 + 3x + -2x2 + -1 + 5x3 = 1 + -1

Reorder the terms:
1 + -1 + 3x + -2x2 + 5x3 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + 3x + -2x2 + 5x3 = 1 + -1
3x + -2x2 + 5x3 = 1 + -1

Combine like terms: 1 + -1 = 0
3x + -2x2 + 5x3 = 0

Solving
3x + -2x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + -2x + 5x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -2x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x + 5x2 = 0

Solving
3 + -2x + 5x2 = 0

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

Divide each side by '5'.
0.6 + -0.4x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.4x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.4x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.4x + x2 = 0 + -0.6
-0.4x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.4x + x2 = -0.6

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = -0.6 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = -0.6 + 0.04

Combine like terms: -0.6 + 0.04 = -0.56
0.04 + -0.4x + x2 = -0.56

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = -0.56

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}