-(n^2+3)=4n

Solution for -(n^2+3)=4n equation:

Simplifying
-1(n2 + 3) = 4n

Reorder the terms:
-1(3 + n2) = 4n
(3 * -1 + n2 * -1) = 4n
(-3 + -1n2) = 4n

Solving
-3 + -1n2 = 4n

Solving for variable 'n'.

Reorder the terms:
-3 + -4n + -1n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
-3 + -4n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 4n + n2) = 0

Factor a trinomial.
-1((3 + n)(1 + n)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
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 = {-3, -1}