4w(3w-6)=3-6w

Solution for 4w(3w-6)=3-6w equation:

Simplifying
4w(3w + -6) = 3 + -6w

Reorder the terms:
4w(-6 + 3w) = 3 + -6w
(-6 * 4w + 3w * 4w) = 3 + -6w
(-24w + 12w2) = 3 + -6w

Solving
-24w + 12w2 = 3 + -6w

Solving for variable 'w'.

Reorder the terms:
-3 + -24w + 6w + 12w2 = 3 + -6w + -3 + 6w

Combine like terms: -24w + 6w = -18w
-3 + -18w + 12w2 = 3 + -6w + -3 + 6w

Reorder the terms:
-3 + -18w + 12w2 = 3 + -3 + -6w + 6w

Combine like terms: 3 + -3 = 0
-3 + -18w + 12w2 = 0 + -6w + 6w
-3 + -18w + 12w2 = -6w + 6w

Combine like terms: -6w + 6w = 0
-3 + -18w + 12w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -6w + 4w2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -6w + 4w2)' equal to zero and attempt to solve:

Simplifying
-1 + -6w + 4w2 = 0

Solving
-1 + -6w + 4w2 = 0

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

Divide each side by '4'.
-0.25 + -1.5w + w2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.5w + 0.25 + w2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.5w + w2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.5w + w2 = 0 + 0.25
-1.5w + w2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.5w + w2 = 0.25

The w term is -1.5w.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5w + 0.5625 + w2 = 0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5w + w2 = 0.25 + 0.5625

Combine like terms: 0.25 + 0.5625 = 0.8125
0.5625 + -1.5w + w2 = 0.8125

Factor a perfect square on the left side:
(w + -0.75)(w + -0.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(w + -0.75) equal to 0.901387819 and -0.901387819.

Subproblem 1
w + -0.75 = 0.901387819

Simplifying
w + -0.75 = 0.901387819

Reorder the terms:
-0.75 + w = 0.901387819

Solving
-0.75 + w = 0.901387819

Solving for variable 'w'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + w = 0.901387819 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + w = 0.901387819 + 0.75
w = 0.901387819 + 0.75

Combine like terms: 0.901387819 + 0.75 = 1.651387819
w = 1.651387819

Simplifying
w = 1.651387819

Subproblem 2
w + -0.75 = -0.901387819

Simplifying
w + -0.75 = -0.901387819

Reorder the terms:
-0.75 + w = -0.901387819

Solving
-0.75 + w = -0.901387819

Solving for variable 'w'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + w = -0.901387819 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + w = -0.901387819 + 0.75
w = -0.901387819 + 0.75

Combine like terms: -0.901387819 + 0.75 = -0.151387819
w = -0.151387819

Simplifying
w = -0.151387819

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.651387819, -0.151387819}
Solution
w = {1.651387819, -0.151387819}