4n^2+7n-57=0

Solution for 4n^2+7n-57=0 equation:

Simplifying
4n2 + 7n + -57 = 0

Reorder the terms:
-57 + 7n + 4n2 = 0

Solving
-57 + 7n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-19 + -4n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-19 + -4n)' equal to zero and attempt to solve:

Simplifying
-19 + -4n = 0

Solving
-19 + -4n = 0

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

Add '19' to each side of the equation.
-19 + 19 + -4n = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -4n = 0 + 19
-4n = 0 + 19

Combine like terms: 0 + 19 = 19
-4n = 19

Divide each side by '-4'.
n = -4.75

Simplifying
n = -4.75
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-4.75, 3}