x^2+12x+41=6

Solution for x^2+12x+41=6 equation:

Simplifying
x2 + 12x + 41 = 6

Reorder the terms:
41 + 12x + x2 = 6

Solving
41 + 12x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
41 + -6 + 12x + x2 = 6 + -6

Combine like terms: 41 + -6 = 35
35 + 12x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
35 + 12x + x2 = 0

Factor a trinomial.
(7 + x)(5 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
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 = {-7, -5}