5n^2=-20-29n

Solution for 5n^2=-20-29n equation:

Simplifying
5n2 = -20 + -29n

Solving
5n2 = -20 + -29n

Solving for variable 'n'.

Reorder the terms:
20 + 29n + 5n2 = -20 + -29n + 20 + 29n

Reorder the terms:
20 + 29n + 5n2 = -20 + 20 + -29n + 29n

Combine like terms: -20 + 20 = 0
20 + 29n + 5n2 = 0 + -29n + 29n
20 + 29n + 5n2 = -29n + 29n

Combine like terms: -29n + 29n = 0
20 + 29n + 5n2 = 0

Factor a trinomial.
(5 + n)(4 + 5n) = 0

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

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

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

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

Simplifying
n = -5
Subproblem 2
Set the factor '(4 + 5n)' equal to zero and attempt to solve:

Simplifying
4 + 5n = 0

Solving
4 + 5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5n = 0 + -4
5n = 0 + -4

Combine like terms: 0 + -4 = -4
5n = -4

Divide each side by '5'.
n = -0.8

Simplifying
n = -0.8
Solution
n = {-5, -0.8}