x^2+4x+1=x+5

Solution for x^2+4x+1=x+5 equation:

Simplifying
x2 + 4x + 1 = x + 5

Reorder the terms:
1 + 4x + x2 = x + 5

Reorder the terms:
1 + 4x + x2 = 5 + x

Solving
1 + 4x + x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
1 + -5 + 4x + -1x + x2 = 5 + x + -5 + -1x

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

Combine like terms: 4x + -1x = 3x
-4 + 3x + x2 = 5 + x + -5 + -1x

Reorder the terms:
-4 + 3x + x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-4 + 3x + x2 = 0 + x + -1x
-4 + 3x + x2 = x + -1x

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

Factor a trinomial.
(-4 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 1}