2L^2-5L=52

Solution for 2L^2-5L=52 equation:

Simplifying
2L2 + -5L = 52

Reorder the terms:
-5L + 2L2 = 52

Solving
-5L + 2L2 = 52

Solving for variable 'L'.

Reorder the terms:
-52 + -5L + 2L2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + -5L + 2L2 = 0

Factor a trinomial.
(-4 + -1L)(13 + -2L) = 0

Subproblem 1
Set the factor '(-4 + -1L)' equal to zero and attempt to solve:

Simplifying
-4 + -1L = 0

Solving
-4 + -1L = 0

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

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

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

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

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

Simplifying
L = -4
Subproblem 2
Set the factor '(13 + -2L)' equal to zero and attempt to solve:

Simplifying
13 + -2L = 0

Solving
13 + -2L = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2L = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2L = 0 + -13
-2L = 0 + -13

Combine like terms: 0 + -13 = -13
-2L = -13

Divide each side by '-2'.
L = 6.5

Simplifying
L = 6.5
Solution
L = {-4, 6.5}