42=l(l+11)

Solution for 42=l(l+11) equation:

Simplifying
42 = l(l + 11)

Reorder the terms:
42 = l(11 + l)
42 = (11 * l + l * l)
42 = (11l + l2)

Solving
42 = 11l + l2

Solving for variable 'l'.

Reorder the terms:
42 + -11l + -1l2 = 11l + -11l + l2 + -1l2

Combine like terms: 11l + -11l = 0
42 + -11l + -1l2 = 0 + l2 + -1l2
42 + -11l + -1l2 = l2 + -1l2

Combine like terms: l2 + -1l2 = 0
42 + -11l + -1l2 = 0

Factor a trinomial.
(3 + -1l)(14 + l) = 0

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 '(14 + l)' equal to zero and attempt to solve:

Simplifying
14 + l = 0

Solving
14 + l = 0

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

Add '-14' to each side of the equation.
14 + -14 + l = 0 + -14

Combine like terms: 14 + -14 = 0
0 + l = 0 + -14
l = 0 + -14

Combine like terms: 0 + -14 = -14
l = -14

Simplifying
l = -14
Solution
l = {3, -14}