3x^2-3x+1=x

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

Simplifying
3x2 + -3x + 1 = x

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

Solving
1 + -3x + 3x2 = x

Solving for variable 'x'.

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

Combine like terms: -3x + -1x = -4x
1 + -4x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
1 + -4x + 3x2 = 0

Factor a trinomial.
(1 + -3x)(1 + -1x) = 0

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.3333333333, 1}