2L^2-5L=12

Solution for 2L^2-5L=12 equation:

Simplifying
2L2 + -5L = 12

Reorder the terms:
-5L + 2L2 = 12

Solving
-5L + 2L2 = 12

Solving for variable 'L'.

Reorder the terms:
-12 + -5L + 2L2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -5L + 2L2 = 0

Factor a trinomial.
(-3 + -2L)(4 + -1L) = 0

Subproblem 1
Set the factor '(-3 + -2L)' equal to zero and attempt to solve:

Simplifying
-3 + -2L = 0

Solving
-3 + -2L = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2L = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2L = 0 + 3
-2L = 0 + 3

Combine like terms: 0 + 3 = 3
-2L = 3

Divide each side by '-2'.
L = -1.5

Simplifying
L = -1.5
Subproblem 2
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
Solution
L = {-1.5, 4}