3w(w-6)-3=-3(-5w+5)-2w

Solution for 3w(w-6)-3=-3(-5w+5)-2w equation:

Simplifying
3w(w + -6) + -3 = -3(-5w + 5) + -2w

Reorder the terms:
3w(-6 + w) + -3 = -3(-5w + 5) + -2w
(-6 * 3w + w * 3w) + -3 = -3(-5w + 5) + -2w
(-18w + 3w2) + -3 = -3(-5w + 5) + -2w

Reorder the terms:
-3 + -18w + 3w2 = -3(-5w + 5) + -2w

Reorder the terms:
-3 + -18w + 3w2 = -3(5 + -5w) + -2w
-3 + -18w + 3w2 = (5 * -3 + -5w * -3) + -2w
-3 + -18w + 3w2 = (-15 + 15w) + -2w

Combine like terms: 15w + -2w = 13w
-3 + -18w + 3w2 = -15 + 13w

Solving
-3 + -18w + 3w2 = -15 + 13w

Solving for variable 'w'.

Reorder the terms:
-3 + 15 + -18w + -13w + 3w2 = -15 + 13w + 15 + -13w

Combine like terms: -3 + 15 = 12
12 + -18w + -13w + 3w2 = -15 + 13w + 15 + -13w

Combine like terms: -18w + -13w = -31w
12 + -31w + 3w2 = -15 + 13w + 15 + -13w

Reorder the terms:
12 + -31w + 3w2 = -15 + 15 + 13w + -13w

Combine like terms: -15 + 15 = 0
12 + -31w + 3w2 = 0 + 13w + -13w
12 + -31w + 3w2 = 13w + -13w

Combine like terms: 13w + -13w = 0
12 + -31w + 3w2 = 0

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

Divide each side by '3'.
4 + -10.33333333w + w2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -10.33333333w + -4 + w2 = 0 + -4

Reorder the terms:
4 + -4 + -10.33333333w + w2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -10.33333333w + w2 = 0 + -4
-10.33333333w + w2 = 0 + -4

Combine like terms: 0 + -4 = -4
-10.33333333w + w2 = -4

The w term is -10.33333333w.  Take half its coefficient (-5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
-10.33333333w + 26.69444443 + w2 = -4 + 26.69444443

Reorder the terms:
26.69444443 + -10.33333333w + w2 = -4 + 26.69444443

Combine like terms: -4 + 26.69444443 = 22.69444443
26.69444443 + -10.33333333w + w2 = 22.69444443

Factor a perfect square on the left side:
(w + -5.166666665)(w + -5.166666665) = 22.69444443

Calculate the square root of the right side: 4.763868641

Break this problem into two subproblems by setting 
(w + -5.166666665) equal to 4.763868641 and -4.763868641.

Subproblem 1
w + -5.166666665 = 4.763868641

Simplifying
w + -5.166666665 = 4.763868641

Reorder the terms:
-5.166666665 + w = 4.763868641

Solving
-5.166666665 + w = 4.763868641

Solving for variable 'w'.

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

Add '5.166666665' to each side of the equation.
-5.166666665 + 5.166666665 + w = 4.763868641 + 5.166666665

Combine like terms: -5.166666665 + 5.166666665 = 0.000000000
0.000000000 + w = 4.763868641 + 5.166666665
w = 4.763868641 + 5.166666665

Combine like terms: 4.763868641 + 5.166666665 = 9.930535306
w = 9.930535306

Simplifying
w = 9.930535306

Subproblem 2
w + -5.166666665 = -4.763868641

Simplifying
w + -5.166666665 = -4.763868641

Reorder the terms:
-5.166666665 + w = -4.763868641

Solving
-5.166666665 + w = -4.763868641

Solving for variable 'w'.

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

Add '5.166666665' to each side of the equation.
-5.166666665 + 5.166666665 + w = -4.763868641 + 5.166666665

Combine like terms: -5.166666665 + 5.166666665 = 0.000000000
0.000000000 + w = -4.763868641 + 5.166666665
w = -4.763868641 + 5.166666665

Combine like terms: -4.763868641 + 5.166666665 = 0.402798024
w = 0.402798024

Simplifying
w = 0.402798024

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {9.930535306, 0.402798024}