250=(w+9)(w-6)2

Solution for 250=(w+9)(w-6)2 equation:

Simplifying
250 = (w + 9)(w + -6) * 2

Reorder the terms:
250 = (9 + w)(w + -6) * 2

Reorder the terms:
250 = (9 + w)(-6 + w) * 2

Reorder the terms for easier multiplication:
250 = 2(9 + w)(-6 + w)

Multiply (9 + w) * (-6 + w)
250 = 2(9(-6 + w) + w(-6 + w))
250 = 2((-6 * 9 + w * 9) + w(-6 + w))
250 = 2((-54 + 9w) + w(-6 + w))
250 = 2(-54 + 9w + (-6 * w + w * w))
250 = 2(-54 + 9w + (-6w + w2))

Combine like terms: 9w + -6w = 3w
250 = 2(-54 + 3w + w2)
250 = (-54 * 2 + 3w * 2 + w2 * 2)
250 = (-108 + 6w + 2w2)

Solving
250 = -108 + 6w + 2w2

Solving for variable 'w'.

Combine like terms: 250 + 108 = 358
358 + -6w + -2w2 = -108 + 6w + 2w2 + 108 + -6w + -2w2

Reorder the terms:
358 + -6w + -2w2 = -108 + 108 + 6w + -6w + 2w2 + -2w2

Combine like terms: -108 + 108 = 0
358 + -6w + -2w2 = 0 + 6w + -6w + 2w2 + -2w2
358 + -6w + -2w2 = 6w + -6w + 2w2 + -2w2

Combine like terms: 6w + -6w = 0
358 + -6w + -2w2 = 0 + 2w2 + -2w2
358 + -6w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
358 + -6w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(179 + -3w + -1w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(179 + -3w + -1w2)' equal to zero and attempt to solve:

Simplifying
179 + -3w + -1w2 = 0

Solving
179 + -3w + -1w2 = 0

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

Divide each side by '-1'.
-179 + 3w + w2 = 0

Move the constant term to the right:

Add '179' to each side of the equation.
-179 + 3w + 179 + w2 = 0 + 179

Reorder the terms:
-179 + 179 + 3w + w2 = 0 + 179

Combine like terms: -179 + 179 = 0
0 + 3w + w2 = 0 + 179
3w + w2 = 0 + 179

Combine like terms: 0 + 179 = 179
3w + w2 = 179

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 = 179 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 179 + 2.25

Combine like terms: 179 + 2.25 = 181.25
2.25 + 3w + w2 = 181.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 181.25

Calculate the square root of the right side: 13.462912018

Break this problem into two subproblems by setting 
(w + 1.5) equal to 13.462912018 and -13.462912018.

Subproblem 1
w + 1.5 = 13.462912018

Simplifying
w + 1.5 = 13.462912018

Reorder the terms:
1.5 + w = 13.462912018

Solving
1.5 + w = 13.462912018

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 = 13.462912018 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 13.462912018 + -1.5
w = 13.462912018 + -1.5

Combine like terms: 13.462912018 + -1.5 = 11.962912018
w = 11.962912018

Simplifying
w = 11.962912018

Subproblem 2
w + 1.5 = -13.462912018

Simplifying
w + 1.5 = -13.462912018

Reorder the terms:
1.5 + w = -13.462912018

Solving
1.5 + w = -13.462912018

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 = -13.462912018 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -13.462912018 + -1.5
w = -13.462912018 + -1.5

Combine like terms: -13.462912018 + -1.5 = -14.962912018
w = -14.962912018

Simplifying
w = -14.962912018

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {11.962912018, -14.962912018}
Solution
w = {11.962912018, -14.962912018}