3w(w-2)=(w+6)(1-w)

Solution for 3w(w-2)=(w+6)(1-w) equation:

Simplifying
3w(w + -2) = (w + 6)(1 + -1w)

Reorder the terms:
3w(-2 + w) = (w + 6)(1 + -1w)
(-2 * 3w + w * 3w) = (w + 6)(1 + -1w)
(-6w + 3w2) = (w + 6)(1 + -1w)

Reorder the terms:
-6w + 3w2 = (6 + w)(1 + -1w)

Multiply (6 + w) * (1 + -1w)
-6w + 3w2 = (6(1 + -1w) + w(1 + -1w))
-6w + 3w2 = ((1 * 6 + -1w * 6) + w(1 + -1w))
-6w + 3w2 = ((6 + -6w) + w(1 + -1w))
-6w + 3w2 = (6 + -6w + (1 * w + -1w * w))
-6w + 3w2 = (6 + -6w + (1w + -1w2))

Combine like terms: -6w + 1w = -5w
-6w + 3w2 = (6 + -5w + -1w2)

Solving
-6w + 3w2 = 6 + -5w + -1w2

Solving for variable 'w'.

Reorder the terms:
-6 + -6w + 5w + 3w2 + w2 = 6 + -5w + -1w2 + -6 + 5w + w2

Combine like terms: -6w + 5w = -1w
-6 + -1w + 3w2 + w2 = 6 + -5w + -1w2 + -6 + 5w + w2

Combine like terms: 3w2 + w2 = 4w2
-6 + -1w + 4w2 = 6 + -5w + -1w2 + -6 + 5w + w2

Reorder the terms:
-6 + -1w + 4w2 = 6 + -6 + -5w + 5w + -1w2 + w2

Combine like terms: 6 + -6 = 0
-6 + -1w + 4w2 = 0 + -5w + 5w + -1w2 + w2
-6 + -1w + 4w2 = -5w + 5w + -1w2 + w2

Combine like terms: -5w + 5w = 0
-6 + -1w + 4w2 = 0 + -1w2 + w2
-6 + -1w + 4w2 = -1w2 + w2

Combine like terms: -1w2 + w2 = 0
-6 + -1w + 4w2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -0.25w + w2 = 0 + 1.5
-0.25w + w2 = 0 + 1.5

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

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 = 1.5 + 0.015625

Reorder the terms:
0.015625 + -0.25w + w2 = 1.5 + 0.015625

Combine like terms: 1.5 + 0.015625 = 1.515625
0.015625 + -0.25w + w2 = 1.515625

Factor a perfect square on the left side:
(w + -0.125)(w + -0.125) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(w + -0.125) equal to 1.231107225 and -1.231107225.

Subproblem 1
w + -0.125 = 1.231107225

Simplifying
w + -0.125 = 1.231107225

Reorder the terms:
-0.125 + w = 1.231107225

Solving
-0.125 + w = 1.231107225

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 = 1.231107225 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + w = 1.231107225 + 0.125
w = 1.231107225 + 0.125

Combine like terms: 1.231107225 + 0.125 = 1.356107225
w = 1.356107225

Simplifying
w = 1.356107225

Subproblem 2
w + -0.125 = -1.231107225

Simplifying
w + -0.125 = -1.231107225

Reorder the terms:
-0.125 + w = -1.231107225

Solving
-0.125 + w = -1.231107225

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 = -1.231107225 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + w = -1.231107225 + 0.125
w = -1.231107225 + 0.125

Combine like terms: -1.231107225 + 0.125 = -1.106107225
w = -1.106107225

Simplifying
w = -1.106107225

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.356107225, -1.106107225}