42+36L-6L^2=96

Solution for 42+36L-6L^2=96 equation:

Simplifying
42 + 36L + -6L2 = 96

Solving
42 + 36L + -6L2 = 96

Solving for variable 'L'.

Reorder the terms:
42 + -96 + 36L + -6L2 = 96 + -96

Combine like terms: 42 + -96 = -54
-54 + 36L + -6L2 = 96 + -96

Combine like terms: 96 + -96 = 0
-54 + 36L + -6L2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + 6L + -1L2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + L)' equal to zero and attempt to solve:

Simplifying
-3 + L = 0

Solving
-3 + L = 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 + L = 0 + 3

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

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

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

Simplifying
3 + -1L = 0

Solving
3 + -1L = 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 + -1L = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1L = 0 + -3
-1L = 0 + -3

Combine like terms: 0 + -3 = -3
-1L = -3

Divide each side by '-1'.
L = 3

Simplifying
L = 3
Solution
L = {3, 3}