2l^2-7l=15

Solution for 2l^2-7l=15 equation:

Simplifying
2l2 + -7l = 15

Reorder the terms:
-7l + 2l2 = 15

Solving
-7l + 2l2 = 15

Solving for variable 'l'.

Reorder the terms:
-15 + -7l + 2l2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -7l + 2l2 = 0

Factor a trinomial.
(-3 + -2l)(5 + -1l) = 0

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

Simplifying
-3 + -2l = 0

Solving
-3 + -2l = 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 + -2l = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2l = 0 + 3
-2l = 0 + 3

Combine like terms: 0 + 3 = 3
-2l = 3

Divide each side by '-2'.
l = -1.5

Simplifying
l = -1.5
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 = {-1.5, 5}