4n^2-37n=30

Solution for 4n^2-37n=30 equation:

Simplifying
4n2 + -37n = 30

Reorder the terms:
-37n + 4n2 = 30

Solving
-37n + 4n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -37n + 4n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -37n + 4n2 = 0

Factor a trinomial.
(-3 + -4n)(10 + -1n) = 0

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

Simplifying
-3 + -4n = 0

Solving
-3 + -4n = 0

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

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

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

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

Divide each side by '-4'.
n = -0.75

Simplifying
n = -0.75
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-0.75, 10}