-5n^2-5=10n

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

Simplifying
-5n2 + -5 = 10n

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

Solving
-5 + -5n2 = 10n

Solving for variable 'n'.

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

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

Factor out the Greatest Common Factor (GCF), '-5'.
-5(1 + 2n + n2) = 0

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

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

Simplifying
1 + n = 0

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

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

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

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

Simplifying
1 + n = 0

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

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

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

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