-2n(2n+3)=4

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

Simplifying
-2n(2n + 3) = 4

Reorder the terms:
-2n(3 + 2n) = 4
(3 * -2n + 2n * -2n) = 4
(-6n + -4n2) = 4

Solving
-6n + -4n2 = 4

Solving for variable 'n'.

Reorder the terms:
-4 + -6n + -4n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -6n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 3n + 2n2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(2 + 3n + 2n2)' equal to zero and attempt to solve:

Simplifying
2 + 3n + 2n2 = 0

Solving
2 + 3n + 2n2 = 0

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

Divide each side by '2'.
1 + 1.5n + n2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.5n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + 1.5n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.5n + n2 = 0 + -1
1.5n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.5n + n2 = -1

The n term is 1.5n.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5n + 0.5625 + n2 = -1 + 0.5625

Reorder the terms:
0.5625 + 1.5n + n2 = -1 + 0.5625

Combine like terms: -1 + 0.5625 = -0.4375
0.5625 + 1.5n + n2 = -0.4375

Factor a perfect square on the left side:
(n + 0.75)(n + 0.75) = -0.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.