l(4l-2)=90

Solution for l(4l-2)=90 equation:

Simplifying
l(4l + -2) = 90

Reorder the terms:
l(-2 + 4l) = 90
(-2 * l + 4l * l) = 90
(-2l + 4l2) = 90

Solving
-2l + 4l2 = 90

Solving for variable 'l'.

Reorder the terms:
-90 + -2l + 4l2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -2l + 4l2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -1l + 2l2) = 0

Factor a trinomial.
2((-9 + -2l)(5 + -1l)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2l)' equal to zero and attempt to solve:

Simplifying
-9 + -2l = 0

Solving
-9 + -2l = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2l = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2l = 0 + 9
-2l = 0 + 9

Combine like terms: 0 + 9 = 9
-2l = 9

Divide each side by '-2'.
l = -4.5

Simplifying
l = -4.5
Subproblem 2
Set the factor '(5 + -1l)' equal to zero and attempt to solve:

Simplifying
5 + -1l = 0

Solving
5 + -1l = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1l = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1l = 0 + -5
-1l = 0 + -5

Combine like terms: 0 + -5 = -5
-1l = -5

Divide each side by '-1'.
l = 5

Simplifying
l = 5
Solution
l = {-4.5, 5}