(4w+4)(w+1)=60

Solution for (4w+4)(w+1)=60 equation:

Simplifying
(4w + 4)(w + 1) = 60

Reorder the terms:
(4 + 4w)(w + 1) = 60

Reorder the terms:
(4 + 4w)(1 + w) = 60

Multiply (4 + 4w) * (1 + w)
(4(1 + w) + 4w * (1 + w)) = 60
((1 * 4 + w * 4) + 4w * (1 + w)) = 60
((4 + 4w) + 4w * (1 + w)) = 60
(4 + 4w + (1 * 4w + w * 4w)) = 60
(4 + 4w + (4w + 4w2)) = 60

Combine like terms: 4w + 4w = 8w
(4 + 8w + 4w2) = 60

Solving
4 + 8w + 4w2 = 60

Solving for variable 'w'.

Reorder the terms:
4 + -60 + 8w + 4w2 = 60 + -60

Combine like terms: 4 + -60 = -56
-56 + 8w + 4w2 = 60 + -60

Combine like terms: 60 + -60 = 0
-56 + 8w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 2w + w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-14 + 2w + w2)' equal to zero and attempt to solve:

Simplifying
-14 + 2w + w2 = 0

Solving
-14 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 2w + 14 + w2 = 0 + 14

Reorder the terms:
-14 + 14 + 2w + w2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 2w + w2 = 0 + 14
2w + w2 = 0 + 14

Combine like terms: 0 + 14 = 14
2w + w2 = 14

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 14 + 1

Reorder the terms:
1 + 2w + w2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + 2w + w2 = 15

Factor a perfect square on the left side:
(w + 1)(w + 1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(w + 1) equal to 3.872983346 and -3.872983346.

Subproblem 1
w + 1 = 3.872983346

Simplifying
w + 1 = 3.872983346

Reorder the terms:
1 + w = 3.872983346

Solving
1 + w = 3.872983346

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + w = 3.872983346 + -1
w = 3.872983346 + -1

Combine like terms: 3.872983346 + -1 = 2.872983346
w = 2.872983346

Simplifying
w = 2.872983346

Subproblem 2
w + 1 = -3.872983346

Simplifying
w + 1 = -3.872983346

Reorder the terms:
1 + w = -3.872983346

Solving
1 + w = -3.872983346

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + w = -3.872983346 + -1
w = -3.872983346 + -1

Combine like terms: -3.872983346 + -1 = -4.872983346
w = -4.872983346

Simplifying
w = -4.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.872983346, -4.872983346}
Solution
w = {2.872983346, -4.872983346}