7n^2+37n+20=4n

Solution for 7n^2+37n+20=4n equation:

Simplifying
7n2 + 37n + 20 = 4n

Reorder the terms:
20 + 37n + 7n2 = 4n

Solving
20 + 37n + 7n2 = 4n

Solving for variable 'n'.

Reorder the terms:
20 + 37n + -4n + 7n2 = 4n + -4n

Combine like terms: 37n + -4n = 33n
20 + 33n + 7n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
20 + 33n + 7n2 = 0

Factor a trinomial.
(4 + n)(5 + 7n) = 0

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

Simplifying
4 + n = 0

Solving
4 + n = 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 + n = 0 + -4

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

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

Simplifying
n = -4
Subproblem 2
Set the factor '(5 + 7n)' equal to zero and attempt to solve:

Simplifying
5 + 7n = 0

Solving
5 + 7n = 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 + 7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7n = 0 + -5
7n = 0 + -5

Combine like terms: 0 + -5 = -5
7n = -5

Divide each side by '7'.
n = -0.7142857143

Simplifying
n = -0.7142857143
Solution
n = {-4, -0.7142857143}