L^2+15L-34=0

Solution for L^2+15L-34=0 equation:

Simplifying
L2 + 15L + -34 = 0

Reorder the terms:
-34 + 15L + L2 = 0

Solving
-34 + 15L + L2 = 0

Solving for variable 'L'.

Factor a trinomial.
(-17 + -1L)(2 + -1L) = 0

Subproblem 1
Set the factor '(-17 + -1L)' equal to zero and attempt to solve:

Simplifying
-17 + -1L = 0

Solving
-17 + -1L = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1L = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1L = 0 + 17
-1L = 0 + 17

Combine like terms: 0 + 17 = 17
-1L = 17

Divide each side by '-1'.
L = -17

Simplifying
L = -17
Subproblem 2
Set the factor '(2 + -1L)' equal to zero and attempt to solve:

Simplifying
2 + -1L = 0

Solving
2 + -1L = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1L = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1L = 0 + -2
-1L = 0 + -2

Combine like terms: 0 + -2 = -2
-1L = -2

Divide each side by '-1'.
L = 2

Simplifying
L = 2
Solution
L = {-17, 2}