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.
(-45 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-45 + -1x)' equal to zero and attempt to solve:

Simplifying
-45 + -1x = 0

Solving
-45 + -1x = 0

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

Add '45' to each side of the equation.
-45 + 45 + -1x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -1x = 0 + 45
-1x = 0 + 45

Combine like terms: 0 + 45 = 45
-1x = 45

Divide each side by '-1'.
x = -45

Simplifying
x = -45
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-45, 4}