2L^2+9L=18

Solution for 2L^2+9L=18 equation:

Simplifying
2L2 + 9L = 18

Reorder the terms:
9L + 2L2 = 18

Solving
9L + 2L2 = 18

Solving for variable 'L'.

Reorder the terms:
-18 + 9L + 2L2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 9L + 2L2 = 0

Factor a trinomial.
(-6 + -1L)(3 + -2L) = 0

Subproblem 1
Set the factor '(-6 + -1L)' equal to zero and attempt to solve:

Simplifying
-6 + -1L = 0

Solving
-6 + -1L = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1L = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1L = 0 + 6
-1L = 0 + 6

Combine like terms: 0 + 6 = 6
-1L = 6

Divide each side by '-1'.
L = -6

Simplifying
L = -6
Subproblem 2
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
Solution
L = {-6, 1.5}