(x*x)+(2x)+(1)=4

Solution for (x*x)+(2x)+(1)=4 equation:

Simplifying
(x * x) + (2x) + (1) = 4

Multiply x * x
(x2) + (2x) + (1) = 4
x2 + (2x) + (1) = 4
x2 + (2x) + 1 = 4

Reorder the terms:
1 + (2x) + x2 = 4

Solving
1 + (2x) + x2 = 4

Solving for variable 'x'.

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

Combine like terms: 1 + -4 = -3
-3 + (2x) + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-3 + (2x) + x2 = 0

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

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 1}