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

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

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

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

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

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

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

Combine like terms: 9w + -6w = 3w
250 = 6(-54 + 3w + w2)
250 = (-54 * 6 + 3w * 6 + w2 * 6)
250 = (-324 + 18w + 6w2)

Solving
250 = -324 + 18w + 6w2

Solving for variable 'w'.

Combine like terms: 250 + 324 = 574
574 + -18w + -6w2 = -324 + 18w + 6w2 + 324 + -18w + -6w2

Reorder the terms:
574 + -18w + -6w2 = -324 + 324 + 18w + -18w + 6w2 + -6w2

Combine like terms: -324 + 324 = 0
574 + -18w + -6w2 = 0 + 18w + -18w + 6w2 + -6w2
574 + -18w + -6w2 = 18w + -18w + 6w2 + -6w2

Combine like terms: 18w + -18w = 0
574 + -18w + -6w2 = 0 + 6w2 + -6w2
574 + -18w + -6w2 = 6w2 + -6w2

Combine like terms: 6w2 + -6w2 = 0
574 + -18w + -6w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(287 + -9w + -3w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(287 + -9w + -3w2)' equal to zero and attempt to solve:

Simplifying
287 + -9w + -3w2 = 0

Solving
287 + -9w + -3w2 = 0

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

Divide each side by '-3'.
-95.66666667 + 3w + w2 = 0

Move the constant term to the right:

Add '95.66666667' to each side of the equation.
-95.66666667 + 3w + 95.66666667 + w2 = 0 + 95.66666667

Reorder the terms:
-95.66666667 + 95.66666667 + 3w + w2 = 0 + 95.66666667

Combine like terms: -95.66666667 + 95.66666667 = 0.00000000
0.00000000 + 3w + w2 = 0 + 95.66666667
3w + w2 = 0 + 95.66666667

Combine like terms: 0 + 95.66666667 = 95.66666667
3w + w2 = 95.66666667

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 = 95.66666667 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 95.66666667 + 2.25

Combine like terms: 95.66666667 + 2.25 = 97.91666667
2.25 + 3w + w2 = 97.91666667

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 97.91666667

Calculate the square root of the right side: 9.895285073

Break this problem into two subproblems by setting 
(w + 1.5) equal to 9.895285073 and -9.895285073.

Subproblem 1
w + 1.5 = 9.895285073

Simplifying
w + 1.5 = 9.895285073

Reorder the terms:
1.5 + w = 9.895285073

Solving
1.5 + w = 9.895285073

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 = 9.895285073 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 9.895285073 + -1.5
w = 9.895285073 + -1.5

Combine like terms: 9.895285073 + -1.5 = 8.395285073
w = 8.395285073

Simplifying
w = 8.395285073

Subproblem 2
w + 1.5 = -9.895285073

Simplifying
w + 1.5 = -9.895285073

Reorder the terms:
1.5 + w = -9.895285073

Solving
1.5 + w = -9.895285073

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 = -9.895285073 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -9.895285073 + -1.5
w = -9.895285073 + -1.5

Combine like terms: -9.895285073 + -1.5 = -11.395285073
w = -11.395285073

Simplifying
w = -11.395285073

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.395285073, -11.395285073}
Solution
w = {8.395285073, -11.395285073}