7n=-10n^2-1

Solution for 7n=-10n^2-1 equation:

Simplifying
7n = -10n2 + -1

Reorder the terms:
7n = -1 + -10n2

Solving
7n = -1 + -10n2

Solving for variable 'n'.

Reorder the terms:
1 + 7n + 10n2 = -1 + -10n2 + 1 + 10n2

Reorder the terms:
1 + 7n + 10n2 = -1 + 1 + -10n2 + 10n2

Combine like terms: -1 + 1 = 0
1 + 7n + 10n2 = 0 + -10n2 + 10n2
1 + 7n + 10n2 = -10n2 + 10n2

Combine like terms: -10n2 + 10n2 = 0
1 + 7n + 10n2 = 0

Factor a trinomial.
(1 + 2n)(1 + 5n) = 0

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

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

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

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

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

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-0.5, -0.2}