2w*2(w+7)=50

Solution for 2w*2(w+7)=50 equation:

Simplifying
2w * 2(w + 7) = 50

Reorder the terms:
2w * 2(7 + w) = 50

Reorder the terms for easier multiplication:
2 * 2w(7 + w) = 50

Multiply 2 * 2
4w(7 + w) = 50
(7 * 4w + w * 4w) = 50
(28w + 4w2) = 50

Solving
28w + 4w2 = 50

Solving for variable 'w'.

Reorder the terms:
-50 + 28w + 4w2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 28w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 14w + 2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-25 + 14w + 2w2)' equal to zero and attempt to solve:

Simplifying
-25 + 14w + 2w2 = 0

Solving
-25 + 14w + 2w2 = 0

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

Divide each side by '2'.
-12.5 + 7w + w2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 7w + 12.5 + w2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 7w + w2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 7w + w2 = 0 + 12.5
7w + w2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
7w + w2 = 12.5

The w term is 7w.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7w + 12.25 + w2 = 12.5 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 12.5 + 12.25

Combine like terms: 12.5 + 12.25 = 24.75
12.25 + 7w + w2 = 24.75

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(w + 3.5) equal to 4.974937186 and -4.974937186.

Subproblem 1
w + 3.5 = 4.974937186

Simplifying
w + 3.5 = 4.974937186

Reorder the terms:
3.5 + w = 4.974937186

Solving
3.5 + w = 4.974937186

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = 4.974937186 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = 4.974937186 + -3.5
w = 4.974937186 + -3.5

Combine like terms: 4.974937186 + -3.5 = 1.474937186
w = 1.474937186

Simplifying
w = 1.474937186

Subproblem 2
w + 3.5 = -4.974937186

Simplifying
w + 3.5 = -4.974937186

Reorder the terms:
3.5 + w = -4.974937186

Solving
3.5 + w = -4.974937186

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = -4.974937186 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = -4.974937186 + -3.5
w = -4.974937186 + -3.5

Combine like terms: -4.974937186 + -3.5 = -8.474937186
w = -8.474937186

Simplifying
w = -8.474937186

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.474937186, -8.474937186}
Solution
w = {1.474937186, -8.474937186}