300=(w)(w+5)(8)

Solution for 300=(w)(w+5)(8) equation:

Simplifying
300 = (w)(w + 5)(8)

Reorder the terms:
300 = w(5 + w)(8)

Reorder the terms for easier multiplication:
300 = 8w(5 + w)
300 = (5 * 8w + w * 8w)
300 = (40w + 8w2)

Solving
300 = 40w + 8w2

Solving for variable 'w'.

Reorder the terms:
300 + -40w + -8w2 = 40w + -40w + 8w2 + -8w2

Combine like terms: 40w + -40w = 0
300 + -40w + -8w2 = 0 + 8w2 + -8w2
300 + -40w + -8w2 = 8w2 + -8w2

Combine like terms: 8w2 + -8w2 = 0
300 + -40w + -8w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(75 + -10w + -2w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(75 + -10w + -2w2)' equal to zero and attempt to solve:

Simplifying
75 + -10w + -2w2 = 0

Solving
75 + -10w + -2w2 = 0

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

Divide each side by '-2'.
-37.5 + 5w + w2 = 0

Move the constant term to the right:

Add '37.5' to each side of the equation.
-37.5 + 5w + 37.5 + w2 = 0 + 37.5

Reorder the terms:
-37.5 + 37.5 + 5w + w2 = 0 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + 5w + w2 = 0 + 37.5
5w + w2 = 0 + 37.5

Combine like terms: 0 + 37.5 = 37.5
5w + w2 = 37.5

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 37.5 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 37.5 + 6.25

Combine like terms: 37.5 + 6.25 = 43.75
6.25 + 5w + w2 = 43.75

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 43.75

Calculate the square root of the right side: 6.614378278

Break this problem into two subproblems by setting 
(w + 2.5) equal to 6.614378278 and -6.614378278.

Subproblem 1
w + 2.5 = 6.614378278

Simplifying
w + 2.5 = 6.614378278

Reorder the terms:
2.5 + w = 6.614378278

Solving
2.5 + w = 6.614378278

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 6.614378278 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 6.614378278 + -2.5
w = 6.614378278 + -2.5

Combine like terms: 6.614378278 + -2.5 = 4.114378278
w = 4.114378278

Simplifying
w = 4.114378278

Subproblem 2
w + 2.5 = -6.614378278

Simplifying
w + 2.5 = -6.614378278

Reorder the terms:
2.5 + w = -6.614378278

Solving
2.5 + w = -6.614378278

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -6.614378278 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -6.614378278 + -2.5
w = -6.614378278 + -2.5

Combine like terms: -6.614378278 + -2.5 = -9.114378278
w = -9.114378278

Simplifying
w = -9.114378278

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.114378278, -9.114378278}
Solution
w = {4.114378278, -9.114378278}