6l^2+2l=48

Solution for 6l^2+2l=48 equation:

Simplifying
6l2 + 2l = 48

Reorder the terms:
2l + 6l2 = 48

Solving
2l + 6l2 = 48

Solving for variable 'l'.

Reorder the terms:
-48 + 2l + 6l2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 2l + 6l2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + l + 3l2) = 0

Factor a trinomial.
2((-3 + -1l)(8 + -3l)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(8 + -3l)' equal to zero and attempt to solve:

Simplifying
8 + -3l = 0

Solving
8 + -3l = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3l = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3l = 0 + -8
-3l = 0 + -8

Combine like terms: 0 + -8 = -8
-3l = -8

Divide each side by '-3'.
l = 2.666666667

Simplifying
l = 2.666666667
Solution
l = {-3, 2.666666667}