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

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

Simplifying
(3 + -1w)(5w + 2) = w

Reorder the terms:
(3 + -1w)(2 + 5w) = w

Multiply (3 + -1w) * (2 + 5w)
(3(2 + 5w) + -1w * (2 + 5w)) = w
((2 * 3 + 5w * 3) + -1w * (2 + 5w)) = w
((6 + 15w) + -1w * (2 + 5w)) = w
(6 + 15w + (2 * -1w + 5w * -1w)) = w
(6 + 15w + (-2w + -5w2)) = w

Combine like terms: 15w + -2w = 13w
(6 + 13w + -5w2) = w

Solving
6 + 13w + -5w2 = w

Solving for variable 'w'.

Reorder the terms:
6 + 13w + -1w + -5w2 = w + -1w

Combine like terms: 13w + -1w = 12w
6 + 12w + -5w2 = w + -1w

Combine like terms: w + -1w = 0
6 + 12w + -5w2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.2 + -2.4w + w2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.4w + 1.2 + w2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.4w + w2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.4w + w2 = 0 + 1.2
-2.4w + w2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.4w + w2 = 1.2

The w term is -2.4w.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4w + 1.44 + w2 = 1.2 + 1.44

Reorder the terms:
1.44 + -2.4w + w2 = 1.2 + 1.44

Combine like terms: 1.2 + 1.44 = 2.64
1.44 + -2.4w + w2 = 2.64

Factor a perfect square on the left side:
(w + -1.2)(w + -1.2) = 2.64

Calculate the square root of the right side: 1.624807681

Break this problem into two subproblems by setting 
(w + -1.2) equal to 1.624807681 and -1.624807681.

Subproblem 1
w + -1.2 = 1.624807681

Simplifying
w + -1.2 = 1.624807681

Reorder the terms:
-1.2 + w = 1.624807681

Solving
-1.2 + w = 1.624807681

Solving for variable 'w'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + w = 1.624807681 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + w = 1.624807681 + 1.2
w = 1.624807681 + 1.2

Combine like terms: 1.624807681 + 1.2 = 2.824807681
w = 2.824807681

Simplifying
w = 2.824807681

Subproblem 2
w + -1.2 = -1.624807681

Simplifying
w + -1.2 = -1.624807681

Reorder the terms:
-1.2 + w = -1.624807681

Solving
-1.2 + w = -1.624807681

Solving for variable 'w'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + w = -1.624807681 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + w = -1.624807681 + 1.2
w = -1.624807681 + 1.2

Combine like terms: -1.624807681 + 1.2 = -0.424807681
w = -0.424807681

Simplifying
w = -0.424807681

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.824807681, -0.424807681}