3(2w+5)w=2

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

Simplifying
3(2w + 5) * w = 2

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

Reorder the terms for easier multiplication:
3w(5 + 2w) = 2
(5 * 3w + 2w * 3w) = 2
(15w + 6w2) = 2

Solving
15w + 6w2 = 2

Solving for variable 'w'.

Reorder the terms:
-2 + 15w + 6w2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 15w + 6w2 = 0

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

Divide each side by '6'.
-0.3333333333 + 2.5w + w2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 2.5w + 0.3333333333 + w2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 2.5w + w2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 2.5w + w2 = 0 + 0.3333333333
2.5w + w2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
2.5w + w2 = 0.3333333333

The w term is 2.5w.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5w + 1.5625 + w2 = 0.3333333333 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 0.3333333333 + 1.5625

Combine like terms: 0.3333333333 + 1.5625 = 1.8958333333
1.5625 + 2.5w + w2 = 1.8958333333

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 1.8958333333

Calculate the square root of the right side: 1.376892637

Break this problem into two subproblems by setting 
(w + 1.25) equal to 1.376892637 and -1.376892637.

Subproblem 1
w + 1.25 = 1.376892637

Simplifying
w + 1.25 = 1.376892637

Reorder the terms:
1.25 + w = 1.376892637

Solving
1.25 + w = 1.376892637

Solving for variable 'w'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + w = 1.376892637 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = 1.376892637 + -1.25
w = 1.376892637 + -1.25

Combine like terms: 1.376892637 + -1.25 = 0.126892637
w = 0.126892637

Simplifying
w = 0.126892637

Subproblem 2
w + 1.25 = -1.376892637

Simplifying
w + 1.25 = -1.376892637

Reorder the terms:
1.25 + w = -1.376892637

Solving
1.25 + w = -1.376892637

Solving for variable 'w'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + w = -1.376892637 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = -1.376892637 + -1.25
w = -1.376892637 + -1.25

Combine like terms: -1.376892637 + -1.25 = -2.626892637
w = -2.626892637

Simplifying
w = -2.626892637

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.126892637, -2.626892637}