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

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

Simplifying
2x2 + 4x + 1 = -1

Reorder the terms:
1 + 4x + 2x2 = -1

Solving
1 + 4x + 2x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 1 + 4x + 2x2 = -1 + 1

Combine like terms: 1 + 1 = 2
2 + 4x + 2x2 = -1 + 1

Combine like terms: -1 + 1 = 0
2 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2x + x2) = 0

Factor a trinomial.
2((1 + x)(1 + x)) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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