n^2+70=-17n

Solution for n^2+70=-17n equation:

Simplifying
n2 + 70 = -17n

Reorder the terms:
70 + n2 = -17n

Solving
70 + n2 = -17n

Solving for variable 'n'.

Reorder the terms:
70 + 17n + n2 = -17n + 17n

Combine like terms: -17n + 17n = 0
70 + 17n + n2 = 0

Factor a trinomial.
(10 + n)(7 + n) = 0

Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 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 + n = 0 + -10

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

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

Simplifying
n = -10
Subproblem 2
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
Solution
n = {-10, -7}