250=(w+9)(w-6)3

Solution for 250=(w+9)(w-6)3 equation:

Simplifying
250 = (w + 9)(w + -6) * 3

Reorder the terms:
250 = (9 + w)(w + -6) * 3

Reorder the terms:
250 = (9 + w)(-6 + w) * 3

Reorder the terms for easier multiplication:
250 = 3(9 + w)(-6 + w)

Multiply (9 + w) * (-6 + w)
250 = 3(9(-6 + w) + w(-6 + w))
250 = 3((-6 * 9 + w * 9) + w(-6 + w))
250 = 3((-54 + 9w) + w(-6 + w))
250 = 3(-54 + 9w + (-6 * w + w * w))
250 = 3(-54 + 9w + (-6w + w2))

Combine like terms: 9w + -6w = 3w
250 = 3(-54 + 3w + w2)
250 = (-54 * 3 + 3w * 3 + w2 * 3)
250 = (-162 + 9w + 3w2)

Solving
250 = -162 + 9w + 3w2

Solving for variable 'w'.

Combine like terms: 250 + 162 = 412
412 + -9w + -3w2 = -162 + 9w + 3w2 + 162 + -9w + -3w2

Reorder the terms:
412 + -9w + -3w2 = -162 + 162 + 9w + -9w + 3w2 + -3w2

Combine like terms: -162 + 162 = 0
412 + -9w + -3w2 = 0 + 9w + -9w + 3w2 + -3w2
412 + -9w + -3w2 = 9w + -9w + 3w2 + -3w2

Combine like terms: 9w + -9w = 0
412 + -9w + -3w2 = 0 + 3w2 + -3w2
412 + -9w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
412 + -9w + -3w2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-137.3333333 + 3w + w2 = 0

Move the constant term to the right:

Add '137.3333333' to each side of the equation.
-137.3333333 + 3w + 137.3333333 + w2 = 0 + 137.3333333

Reorder the terms:
-137.3333333 + 137.3333333 + 3w + w2 = 0 + 137.3333333

Combine like terms: -137.3333333 + 137.3333333 = 0.0000000
0.0000000 + 3w + w2 = 0 + 137.3333333
3w + w2 = 0 + 137.3333333

Combine like terms: 0 + 137.3333333 = 137.3333333
3w + w2 = 137.3333333

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 = 137.3333333 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 137.3333333 + 2.25

Combine like terms: 137.3333333 + 2.25 = 139.5833333
2.25 + 3w + w2 = 139.5833333

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 139.5833333

Calculate the square root of the right side: 11.814539064

Break this problem into two subproblems by setting 
(w + 1.5) equal to 11.814539064 and -11.814539064.

Subproblem 1
w + 1.5 = 11.814539064

Simplifying
w + 1.5 = 11.814539064

Reorder the terms:
1.5 + w = 11.814539064

Solving
1.5 + w = 11.814539064

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 = 11.814539064 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 11.814539064 + -1.5
w = 11.814539064 + -1.5

Combine like terms: 11.814539064 + -1.5 = 10.314539064
w = 10.314539064

Simplifying
w = 10.314539064

Subproblem 2
w + 1.5 = -11.814539064

Simplifying
w + 1.5 = -11.814539064

Reorder the terms:
1.5 + w = -11.814539064

Solving
1.5 + w = -11.814539064

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 = -11.814539064 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -11.814539064 + -1.5
w = -11.814539064 + -1.5

Combine like terms: -11.814539064 + -1.5 = -13.314539064
w = -13.314539064

Simplifying
w = -13.314539064

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.314539064, -13.314539064}