2w(4+w)+4(5w-3)=

Solution for 2w(4+w)+4(5w-3)= equation:

Simplifying
2w(4 + w) + 4(5w + -3) = 0
(4 * 2w + w * 2w) + 4(5w + -3) = 0
(8w + 2w2) + 4(5w + -3) = 0

Reorder the terms:
8w + 2w2 + 4(-3 + 5w) = 0
8w + 2w2 + (-3 * 4 + 5w * 4) = 0
8w + 2w2 + (-12 + 20w) = 0

Reorder the terms:
-12 + 8w + 20w + 2w2 = 0

Combine like terms: 8w + 20w = 28w
-12 + 28w + 2w2 = 0

Solving
-12 + 28w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 14w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 14w + w2)' equal to zero and attempt to solve:

Simplifying
-6 + 14w + w2 = 0

Solving
-6 + 14w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 14w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + 14w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 14w + w2 = 0 + 6
14w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
14w + w2 = 6

The w term is 14w.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14w + 49 + w2 = 6 + 49

Reorder the terms:
49 + 14w + w2 = 6 + 49

Combine like terms: 6 + 49 = 55
49 + 14w + w2 = 55

Factor a perfect square on the left side:
(w + 7)(w + 7) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(w + 7) equal to 7.416198487 and -7.416198487.

Subproblem 1
w + 7 = 7.416198487

Simplifying
w + 7 = 7.416198487

Reorder the terms:
7 + w = 7.416198487

Solving
7 + w = 7.416198487

Solving for variable 'w'.

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

Add '-7' to each side of the equation.
7 + -7 + w = 7.416198487 + -7

Combine like terms: 7 + -7 = 0
0 + w = 7.416198487 + -7
w = 7.416198487 + -7

Combine like terms: 7.416198487 + -7 = 0.416198487
w = 0.416198487

Simplifying
w = 0.416198487

Subproblem 2
w + 7 = -7.416198487

Simplifying
w + 7 = -7.416198487

Reorder the terms:
7 + w = -7.416198487

Solving
7 + w = -7.416198487

Solving for variable 'w'.

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

Add '-7' to each side of the equation.
7 + -7 + w = -7.416198487 + -7

Combine like terms: 7 + -7 = 0
0 + w = -7.416198487 + -7
w = -7.416198487 + -7

Combine like terms: -7.416198487 + -7 = -14.416198487
w = -14.416198487

Simplifying
w = -14.416198487

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.416198487, -14.416198487}
Solution
w = {0.416198487, -14.416198487}