4n^2+12n-24=0

Solution for 4n^2+12n-24=0 equation:

Simplifying
4n2 + 12n + -24 = 0

Reorder the terms:
-24 + 12n + 4n2 = 0

Solving
-24 + 12n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 3n + n2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + 3n + n2)' equal to zero and attempt to solve:

Simplifying
-6 + 3n + n2 = 0

Solving
-6 + 3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + 3n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3n + n2 = 0 + 6
3n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
3n + n2 = 6

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 6 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3n + n2 = 8.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(n + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
n + 1.5 = 2.872281323

Simplifying
n + 1.5 = 2.872281323

Reorder the terms:
1.5 + n = 2.872281323

Solving
1.5 + n = 2.872281323

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 2.872281323 + -1.5
n = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
n = 1.372281323

Simplifying
n = 1.372281323

Subproblem 2
n + 1.5 = -2.872281323

Simplifying
n + 1.5 = -2.872281323

Reorder the terms:
1.5 + n = -2.872281323

Solving
1.5 + n = -2.872281323

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -2.872281323 + -1.5
n = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
n = -4.372281323

Simplifying
n = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.372281323, -4.372281323}
Solution
n = {1.372281323, -4.372281323}