x^2+41x+180=0

Solution for x^2+41x+180=0 equation:

Simplifying
x2 + 41x + 180 = 0

Reorder the terms:
180 + 41x + x2 = 0

Solving
180 + 41x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(36 + x)' equal to zero and attempt to solve:

Simplifying
36 + x = 0

Solving
36 + x = 0

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

Add '-36' to each side of the equation.
36 + -36 + x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + x = 0 + -36
x = 0 + -36

Combine like terms: 0 + -36 = -36
x = -36

Simplifying
x = -36
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 = {-36, -5}