5n^2-n+4=10

Solution for 5n^2-n+4=10 equation:

Simplifying
5n2 + -1n + 4 = 10

Reorder the terms:
4 + -1n + 5n2 = 10

Solving
4 + -1n + 5n2 = 10

Solving for variable 'n'.

Reorder the terms:
4 + -10 + -1n + 5n2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + -1n + 5n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + -1n + 5n2 = 0

Factor a trinomial.
(-1 + -1n)(6 + -5n) = 0

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {-1, 1.2}