24=2(2+w)2w

Solution for 24=2(2+w)2w equation:

Simplifying
24 = 2(2 + w) * 2w

Reorder the terms for easier multiplication:
24 = 2 * 2w(2 + w)

Multiply 2 * 2
24 = 4w(2 + w)
24 = (2 * 4w + w * 4w)
24 = (8w + 4w2)

Solving
24 = 8w + 4w2

Solving for variable 'w'.

Reorder the terms:
24 + -8w + -4w2 = 8w + -8w + 4w2 + -4w2

Combine like terms: 8w + -8w = 0
24 + -8w + -4w2 = 0 + 4w2 + -4w2
24 + -8w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
24 + -8w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -2w + -1w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -2w + -1w2)' equal to zero and attempt to solve:

Simplifying
6 + -2w + -1w2 = 0

Solving
6 + -2w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 2w + w2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + 2w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2w + w2 = 0 + 6
2w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
2w + w2 = 6

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 6 + 1

Reorder the terms:
1 + 2w + w2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2w + w2 = 7

Factor a perfect square on the left side:
(w + 1)(w + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(w + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
w + 1 = 2.645751311

Simplifying
w + 1 = 2.645751311

Reorder the terms:
1 + w = 2.645751311

Solving
1 + w = 2.645751311

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + w = 2.645751311 + -1
w = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
w = 1.645751311

Simplifying
w = 1.645751311

Subproblem 2
w + 1 = -2.645751311

Simplifying
w + 1 = -2.645751311

Reorder the terms:
1 + w = -2.645751311

Solving
1 + w = -2.645751311

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + w = -2.645751311 + -1
w = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
w = -3.645751311

Simplifying
w = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.645751311, -3.645751311}
Solution
w = {1.645751311, -3.645751311}