0.75+0.75(w+0.75)+12=2w(3w+4w)

Solution for 0.75+0.75(w+0.75)+12=2w(3w+4w) equation:

Simplifying
0.75 + 0.75(w + 0.75) + 12 = 2w(3w + 4w)

Reorder the terms:
0.75 + 0.75(0.75 + w) + 12 = 2w(3w + 4w)
0.75 + (0.75 * 0.75 + w * 0.75) + 12 = 2w(3w + 4w)
0.75 + (0.5625 + 0.75w) + 12 = 2w(3w + 4w)

Reorder the terms:
0.75 + 0.5625 + 12 + 0.75w = 2w(3w + 4w)

Combine like terms: 0.75 + 0.5625 = 1.3125
1.3125 + 12 + 0.75w = 2w(3w + 4w)

Combine like terms: 1.3125 + 12 = 13.3125
13.3125 + 0.75w = 2w(3w + 4w)

Combine like terms: 3w + 4w = 7w
13.3125 + 0.75w = 2w(7w)

Remove parenthesis around (7w)
13.3125 + 0.75w = 2w * 7w

Reorder the terms for easier multiplication:
13.3125 + 0.75w = 2 * 7w * w

Multiply 2 * 7
13.3125 + 0.75w = 14w * w

Multiply w * w
13.3125 + 0.75w = 14w2

Solving
13.3125 + 0.75w = 14w2

Solving for variable 'w'.

Combine like terms: 14w2 + -14w2 = 0
13.3125 + 0.75w + -14w2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-0.9508928571 + -0.05357142857w + w2 = 0

Move the constant term to the right:

Add '0.9508928571' to each side of the equation.
-0.9508928571 + -0.05357142857w + 0.9508928571 + w2 = 0 + 0.9508928571

Reorder the terms:
-0.9508928571 + 0.9508928571 + -0.05357142857w + w2 = 0 + 0.9508928571

Combine like terms: -0.9508928571 + 0.9508928571 = 0.0000000000
0.0000000000 + -0.05357142857w + w2 = 0 + 0.9508928571
-0.05357142857w + w2 = 0 + 0.9508928571

Combine like terms: 0 + 0.9508928571 = 0.9508928571
-0.05357142857w + w2 = 0.9508928571

The w term is -0.05357142857w.  Take half its coefficient (-0.02678571429).
Square it (0.0007174744900) and add it to both sides.

Add '0.0007174744900' to each side of the equation.
-0.05357142857w + 0.0007174744900 + w2 = 0.9508928571 + 0.0007174744900

Reorder the terms:
0.0007174744900 + -0.05357142857w + w2 = 0.9508928571 + 0.0007174744900

Combine like terms: 0.9508928571 + 0.0007174744900 = 0.95161033159
0.0007174744900 + -0.05357142857w + w2 = 0.95161033159

Factor a perfect square on the left side:
(w + -0.02678571429)(w + -0.02678571429) = 0.95161033159

Calculate the square root of the right side: 0.975505167

Break this problem into two subproblems by setting 
(w + -0.02678571429) equal to 0.975505167 and -0.975505167.

Subproblem 1
w + -0.02678571429 = 0.975505167

Simplifying
w + -0.02678571429 = 0.975505167

Reorder the terms:
-0.02678571429 + w = 0.975505167

Solving
-0.02678571429 + w = 0.975505167

Solving for variable 'w'.

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

Add '0.02678571429' to each side of the equation.
-0.02678571429 + 0.02678571429 + w = 0.975505167 + 0.02678571429

Combine like terms: -0.02678571429 + 0.02678571429 = 0.00000000000
0.00000000000 + w = 0.975505167 + 0.02678571429
w = 0.975505167 + 0.02678571429

Combine like terms: 0.975505167 + 0.02678571429 = 1.00229088129
w = 1.00229088129

Simplifying
w = 1.00229088129

Subproblem 2
w + -0.02678571429 = -0.975505167

Simplifying
w + -0.02678571429 = -0.975505167

Reorder the terms:
-0.02678571429 + w = -0.975505167

Solving
-0.02678571429 + w = -0.975505167

Solving for variable 'w'.

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

Add '0.02678571429' to each side of the equation.
-0.02678571429 + 0.02678571429 + w = -0.975505167 + 0.02678571429

Combine like terms: -0.02678571429 + 0.02678571429 = 0.00000000000
0.00000000000 + w = -0.975505167 + 0.02678571429
w = -0.975505167 + 0.02678571429

Combine like terms: -0.975505167 + 0.02678571429 = -0.94871945271
w = -0.94871945271

Simplifying
w = -0.94871945271

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.00229088129, -0.94871945271}