12n(n+3)=5n-20

Solution for 12n(n+3)=5n-20 equation:

Simplifying
12n(n + 3) = 5n + -20

Reorder the terms:
12n(3 + n) = 5n + -20
(3 * 12n + n * 12n) = 5n + -20
(36n + 12n2) = 5n + -20

Reorder the terms:
36n + 12n2 = -20 + 5n

Solving
36n + 12n2 = -20 + 5n

Solving for variable 'n'.

Reorder the terms:
20 + 36n + -5n + 12n2 = -20 + 5n + 20 + -5n

Combine like terms: 36n + -5n = 31n
20 + 31n + 12n2 = -20 + 5n + 20 + -5n

Reorder the terms:
20 + 31n + 12n2 = -20 + 20 + 5n + -5n

Combine like terms: -20 + 20 = 0
20 + 31n + 12n2 = 0 + 5n + -5n
20 + 31n + 12n2 = 5n + -5n

Combine like terms: 5n + -5n = 0
20 + 31n + 12n2 = 0

Factor a trinomial.
(4 + 3n)(5 + 4n) = 0

Subproblem 1
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Subproblem 2
Set the factor '(5 + 4n)' equal to zero and attempt to solve:

Simplifying
5 + 4n = 0

Solving
5 + 4n = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4n = 0 + -5
4n = 0 + -5

Combine like terms: 0 + -5 = -5
4n = -5

Divide each side by '4'.
n = -1.25

Simplifying
n = -1.25
Solution
n = {-1.333333333, -1.25}