2w*2(7w-2)=60

Solution for 2w*2(7w-2)=60 equation:

Simplifying
2w * 2(7w + -2) = 60

Reorder the terms:
2w * 2(-2 + 7w) = 60

Reorder the terms for easier multiplication:
2 * 2w(-2 + 7w) = 60

Multiply 2 * 2
4w(-2 + 7w) = 60
(-2 * 4w + 7w * 4w) = 60
(-8w + 28w2) = 60

Solving
-8w + 28w2 = 60

Solving for variable 'w'.

Reorder the terms:
-60 + -8w + 28w2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -8w + 28w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -2w + 7w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-15 + -2w + 7w2)' equal to zero and attempt to solve:

Simplifying
-15 + -2w + 7w2 = 0

Solving
-15 + -2w + 7w2 = 0

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

Divide each side by '7'.
-2.142857143 + -0.2857142857w + w2 = 0

Move the constant term to the right:

Add '2.142857143' to each side of the equation.
-2.142857143 + -0.2857142857w + 2.142857143 + w2 = 0 + 2.142857143

Reorder the terms:
-2.142857143 + 2.142857143 + -0.2857142857w + w2 = 0 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + -0.2857142857w + w2 = 0 + 2.142857143
-0.2857142857w + w2 = 0 + 2.142857143

Combine like terms: 0 + 2.142857143 = 2.142857143
-0.2857142857w + w2 = 2.142857143

The w term is -0.2857142857w.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857w + 0.02040816328 + w2 = 2.142857143 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857w + w2 = 2.142857143 + 0.02040816328

Combine like terms: 2.142857143 + 0.02040816328 = 2.16326530628
0.02040816328 + -0.2857142857w + w2 = 2.16326530628

Factor a perfect square on the left side:
(w + -0.1428571429)(w + -0.1428571429) = 2.16326530628

Calculate the square root of the right side: 1.470804306

Break this problem into two subproblems by setting 
(w + -0.1428571429) equal to 1.470804306 and -1.470804306.

Subproblem 1
w + -0.1428571429 = 1.470804306

Simplifying
w + -0.1428571429 = 1.470804306

Reorder the terms:
-0.1428571429 + w = 1.470804306

Solving
-0.1428571429 + w = 1.470804306

Solving for variable 'w'.

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

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.1428571429 + w = 1.470804306 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + w = 1.470804306 + 0.1428571429
w = 1.470804306 + 0.1428571429

Combine like terms: 1.470804306 + 0.1428571429 = 1.6136614489
w = 1.6136614489

Simplifying
w = 1.6136614489

Subproblem 2
w + -0.1428571429 = -1.470804306

Simplifying
w + -0.1428571429 = -1.470804306

Reorder the terms:
-0.1428571429 + w = -1.470804306

Solving
-0.1428571429 + w = -1.470804306

Solving for variable 'w'.

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

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.1428571429 + w = -1.470804306 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + w = -1.470804306 + 0.1428571429
w = -1.470804306 + 0.1428571429

Combine like terms: -1.470804306 + 0.1428571429 = -1.3279471631
w = -1.3279471631

Simplifying
w = -1.3279471631

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.6136614489, -1.3279471631}
Solution
w = {1.6136614489, -1.3279471631}