L^2-3L-180=0

Solution for L^2-3L-180=0 equation:

Simplifying
L2 + -3L + -180 = 0

Reorder the terms:
-180 + -3L + L2 = 0

Solving
-180 + -3L + L2 = 0

Solving for variable 'L'.

Factor a trinomial.
(-12 + -1L)(15 + -1L) = 0

Subproblem 1
Set the factor '(-12 + -1L)' equal to zero and attempt to solve:

Simplifying
-12 + -1L = 0

Solving
-12 + -1L = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1L = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1L = 0 + 12
-1L = 0 + 12

Combine like terms: 0 + 12 = 12
-1L = 12

Divide each side by '-1'.
L = -12

Simplifying
L = -12
Subproblem 2
Set the factor '(15 + -1L)' equal to zero and attempt to solve:

Simplifying
15 + -1L = 0

Solving
15 + -1L = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1L = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1L = 0 + -15
-1L = 0 + -15

Combine like terms: 0 + -15 = -15
-1L = -15

Divide each side by '-1'.
L = 15

Simplifying
L = 15
Solution
L = {-12, 15}