5n^2-14n-75=-4n

Solution for 5n^2-14n-75=-4n equation:

Simplifying
5n2 + -14n + -75 = -4n

Reorder the terms:
-75 + -14n + 5n2 = -4n

Solving
-75 + -14n + 5n2 = -4n

Solving for variable 'n'.

Reorder the terms:
-75 + -14n + 4n + 5n2 = -4n + 4n

Combine like terms: -14n + 4n = -10n
-75 + -10n + 5n2 = -4n + 4n

Combine like terms: -4n + 4n = 0
-75 + -10n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + -2n + n2) = 0

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

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-3, 5}