n^2+14n-5=10

Solution for n^2+14n-5=10 equation:

Simplifying
n2 + 14n + -5 = 10

Reorder the terms:
-5 + 14n + n2 = 10

Solving
-5 + 14n + n2 = 10

Solving for variable 'n'.

Reorder the terms:
-5 + -10 + 14n + n2 = 10 + -10

Combine like terms: -5 + -10 = -15
-15 + 14n + n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-15 + 14n + n2 = 0

Factor a trinomial.
(-15 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying
-15 + -1n = 0

Solving
-15 + -1n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1n = 0 + 15
-1n = 0 + 15

Combine like terms: 0 + 15 = 15
-1n = 15

Divide each side by '-1'.
n = -15

Simplifying
n = -15
Subproblem 2
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
Solution
n = {-15, 1}