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

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

Simplifying
2(w + 3) * 2w + 3 = w + 1

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

Reorder the terms for easier multiplication:
2 * 2w(3 + w) + 3 = w + 1

Multiply 2 * 2
4w(3 + w) + 3 = w + 1
(3 * 4w + w * 4w) + 3 = w + 1
(12w + 4w2) + 3 = w + 1

Reorder the terms:
3 + 12w + 4w2 = w + 1

Reorder the terms:
3 + 12w + 4w2 = 1 + w

Solving
3 + 12w + 4w2 = 1 + w

Solving for variable 'w'.

Reorder the terms:
3 + -1 + 12w + -1w + 4w2 = 1 + w + -1 + -1w

Combine like terms: 3 + -1 = 2
2 + 12w + -1w + 4w2 = 1 + w + -1 + -1w

Combine like terms: 12w + -1w = 11w
2 + 11w + 4w2 = 1 + w + -1 + -1w

Reorder the terms:
2 + 11w + 4w2 = 1 + -1 + w + -1w

Combine like terms: 1 + -1 = 0
2 + 11w + 4w2 = 0 + w + -1w
2 + 11w + 4w2 = w + -1w

Combine like terms: w + -1w = 0
2 + 11w + 4w2 = 0

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

Divide each side by '4'.
0.5 + 2.75w + w2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.75w + -0.5 + w2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.75w + w2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.75w + w2 = 0 + -0.5
2.75w + w2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.75w + w2 = -0.5

The w term is 2.75w.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75w + 1.890625 + w2 = -0.5 + 1.890625

Reorder the terms:
1.890625 + 2.75w + w2 = -0.5 + 1.890625

Combine like terms: -0.5 + 1.890625 = 1.390625
1.890625 + 2.75w + w2 = 1.390625

Factor a perfect square on the left side:
(w + 1.375)(w + 1.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(w + 1.375) equal to 1.179247642 and -1.179247642.

Subproblem 1
w + 1.375 = 1.179247642

Simplifying
w + 1.375 = 1.179247642

Reorder the terms:
1.375 + w = 1.179247642

Solving
1.375 + w = 1.179247642

Solving for variable 'w'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + w = 1.179247642 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + w = 1.179247642 + -1.375
w = 1.179247642 + -1.375

Combine like terms: 1.179247642 + -1.375 = -0.195752358
w = -0.195752358

Simplifying
w = -0.195752358

Subproblem 2
w + 1.375 = -1.179247642

Simplifying
w + 1.375 = -1.179247642

Reorder the terms:
1.375 + w = -1.179247642

Solving
1.375 + w = -1.179247642

Solving for variable 'w'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + w = -1.179247642 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + w = -1.179247642 + -1.375
w = -1.179247642 + -1.375

Combine like terms: -1.179247642 + -1.375 = -2.554247642
w = -2.554247642

Simplifying
w = -2.554247642

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.195752358, -2.554247642}