x^2+4x+1=-3

Solution for x^2+4x+1=-3 equation:

Simplifying
x2 + 4x + 1 = -3

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

Solving
1 + 4x + x2 = -3

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(2 + x)(2 + x) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-2, -2}