5n^2+12n=-8

Solution for 5n^2+12n=-8 equation:

Simplifying
5n2 + 12n = -8

Reorder the terms:
12n + 5n2 = -8

Solving
12n + 5n2 = -8

Solving for variable 'n'.

Reorder the terms:
8 + 12n + 5n2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 12n + 5n2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.6 + 2.4n + n2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 2.4n + -1.6 + n2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 2.4n + n2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 2.4n + n2 = 0 + -1.6
2.4n + n2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
2.4n + n2 = -1.6

The n term is 2.4n.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4n + 1.44 + n2 = -1.6 + 1.44

Reorder the terms:
1.44 + 2.4n + n2 = -1.6 + 1.44

Combine like terms: -1.6 + 1.44 = -0.16
1.44 + 2.4n + n2 = -0.16

Factor a perfect square on the left side:
(n + 1.2)(n + 1.2) = -0.16

Can't calculate square root of the right side.

The solution to this equation could not be determined.