4(4w-1)(2w+1)=30

Solution for 4(4w-1)(2w+1)=30 equation:

Simplifying
4(4w + -1)(2w + 1) = 30

Reorder the terms:
4(-1 + 4w)(2w + 1) = 30

Reorder the terms:
4(-1 + 4w)(1 + 2w) = 30

Multiply (-1 + 4w) * (1 + 2w)
4(-1(1 + 2w) + 4w * (1 + 2w)) = 30
4((1 * -1 + 2w * -1) + 4w * (1 + 2w)) = 30
4((-1 + -2w) + 4w * (1 + 2w)) = 30
4(-1 + -2w + (1 * 4w + 2w * 4w)) = 30
4(-1 + -2w + (4w + 8w2)) = 30

Combine like terms: -2w + 4w = 2w
4(-1 + 2w + 8w2) = 30
(-1 * 4 + 2w * 4 + 8w2 * 4) = 30
(-4 + 8w + 32w2) = 30

Solving
-4 + 8w + 32w2 = 30

Solving for variable 'w'.

Reorder the terms:
-4 + -30 + 8w + 32w2 = 30 + -30

Combine like terms: -4 + -30 = -34
-34 + 8w + 32w2 = 30 + -30

Combine like terms: 30 + -30 = 0
-34 + 8w + 32w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 4w + 16w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 4w + 16w2)' equal to zero and attempt to solve:

Simplifying
-17 + 4w + 16w2 = 0

Solving
-17 + 4w + 16w2 = 0

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

Divide each side by '16'.
-1.0625 + 0.25w + w2 = 0

Move the constant term to the right:

Add '1.0625' to each side of the equation.
-1.0625 + 0.25w + 1.0625 + w2 = 0 + 1.0625

Reorder the terms:
-1.0625 + 1.0625 + 0.25w + w2 = 0 + 1.0625

Combine like terms: -1.0625 + 1.0625 = 0.0000
0.0000 + 0.25w + w2 = 0 + 1.0625
0.25w + w2 = 0 + 1.0625

Combine like terms: 0 + 1.0625 = 1.0625
0.25w + w2 = 1.0625

The w term is 0.25w.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25w + 0.015625 + w2 = 1.0625 + 0.015625

Reorder the terms:
0.015625 + 0.25w + w2 = 1.0625 + 0.015625

Combine like terms: 1.0625 + 0.015625 = 1.078125
0.015625 + 0.25w + w2 = 1.078125

Factor a perfect square on the left side:
(w + 0.125)(w + 0.125) = 1.078125

Calculate the square root of the right side: 1.038327983

Break this problem into two subproblems by setting 
(w + 0.125) equal to 1.038327983 and -1.038327983.

Subproblem 1
w + 0.125 = 1.038327983

Simplifying
w + 0.125 = 1.038327983

Reorder the terms:
0.125 + w = 1.038327983

Solving
0.125 + w = 1.038327983

Solving for variable 'w'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + w = 1.038327983 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + w = 1.038327983 + -0.125
w = 1.038327983 + -0.125

Combine like terms: 1.038327983 + -0.125 = 0.913327983
w = 0.913327983

Simplifying
w = 0.913327983

Subproblem 2
w + 0.125 = -1.038327983

Simplifying
w + 0.125 = -1.038327983

Reorder the terms:
0.125 + w = -1.038327983

Solving
0.125 + w = -1.038327983

Solving for variable 'w'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + w = -1.038327983 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + w = -1.038327983 + -0.125
w = -1.038327983 + -0.125

Combine like terms: -1.038327983 + -0.125 = -1.163327983
w = -1.163327983

Simplifying
w = -1.163327983

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.913327983, -1.163327983}
Solution
w = {0.913327983, -1.163327983}