4w^2-12w-24=0

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

Simplifying
4w2 + -12w + -24 = 0

Reorder the terms:
-24 + -12w + 4w2 = 0

Solving
-24 + -12w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -3w + w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -3w + w2)' equal to zero and attempt to solve:

Simplifying
-6 + -3w + w2 = 0

Solving
-6 + -3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + -3w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3w + w2 = 0 + 6
-3w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3w + w2 = 6

The w term is -3w.  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.
-3w + 2.25 + w2 = 6 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + -3w + w2 = 8.25

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

Calculate the square root of the right side: 2.872281323

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

Subproblem 1
w + -1.5 = 2.872281323

Simplifying
w + -1.5 = 2.872281323

Reorder the terms:
-1.5 + w = 2.872281323

Solving
-1.5 + w = 2.872281323

Solving for variable 'w'.

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

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

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

Combine like terms: 2.872281323 + 1.5 = 4.372281323
w = 4.372281323

Simplifying
w = 4.372281323

Subproblem 2
w + -1.5 = -2.872281323

Simplifying
w + -1.5 = -2.872281323

Reorder the terms:
-1.5 + w = -2.872281323

Solving
-1.5 + w = -2.872281323

Solving for variable 'w'.

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

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

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

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

Simplifying
w = -1.372281323

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