12n+3=-12n^2

Solution for 12n+3=-12n^2 equation:

Simplifying
12n + 3 = -12n2

Reorder the terms:
3 + 12n = -12n2

Solving
3 + 12n = -12n2

Solving for variable 'n'.

Combine like terms: -12n2 + 12n2 = 0
3 + 12n + 12n2 = 0

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

Factor a trinomial.
3((1 + 2n)(1 + 2n)) = 0

Ignore the factor 3.
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 + 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
Solution
n = {-0.5, -0.5}