x^2-4x+1=x+1

Solution for x^2-4x+1=x+1 equation:

Simplifying
x2 + -4x + 1 = x + 1

Reorder the terms:
1 + -4x + x2 = x + 1

Reorder the terms:
1 + -4x + x2 = 1 + x

Add '-1' to each side of the equation.
1 + -4x + -1 + x2 = 1 + -1 + x

Reorder the terms:
1 + -1 + -4x + x2 = 1 + -1 + x

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

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

Solving
-4x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-4x + -1x + x2 = x + -1x

Combine like terms: -4x + -1x = -5x
-5x + x2 = x + -1x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + x) = 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 '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Solution
x = {0, 5}