L(3L-7)=20

Solution for L(3L-7)=20 equation:

Simplifying
L(3L + -7) = 20

Reorder the terms:
L(-7 + 3L) = 20
(-7 * L + 3L * L) = 20
(-7L + 3L2) = 20

Solving
-7L + 3L2 = 20

Solving for variable 'L'.

Reorder the terms:
-20 + -7L + 3L2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -7L + 3L2 = 0

Factor a trinomial.
(-5 + -3L)(4 + -1L) = 0

Subproblem 1
Set the factor '(-5 + -3L)' equal to zero and attempt to solve:

Simplifying
-5 + -3L = 0

Solving
-5 + -3L = 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 + -3L = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3L = 0 + 5
-3L = 0 + 5

Combine like terms: 0 + 5 = 5
-3L = 5

Divide each side by '-3'.
L = -1.666666667

Simplifying
L = -1.666666667
Subproblem 2
Set the factor '(4 + -1L)' equal to zero and attempt to solve:

Simplifying
4 + -1L = 0

Solving
4 + -1L = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1L = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1L = 0 + -4
-1L = 0 + -4

Combine like terms: 0 + -4 = -4
-1L = -4

Divide each side by '-1'.
L = 4

Simplifying
L = 4
Solution
L = {-1.666666667, 4}