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

Solution for 3(2w+1)2(w-2)=5 equation:

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

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

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

Reorder the terms for easier multiplication:
3 * 2(1 + 2w)(-2 + w) = 5

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

Multiply (1 + 2w) * (-2 + w)
6(1(-2 + w) + 2w * (-2 + w)) = 5
6((-2 * 1 + w * 1) + 2w * (-2 + w)) = 5
6((-2 + 1w) + 2w * (-2 + w)) = 5
6(-2 + 1w + (-2 * 2w + w * 2w)) = 5
6(-2 + 1w + (-4w + 2w2)) = 5

Combine like terms: 1w + -4w = -3w
6(-2 + -3w + 2w2) = 5
(-2 * 6 + -3w * 6 + 2w2 * 6) = 5
(-12 + -18w + 12w2) = 5

Solving
-12 + -18w + 12w2 = 5

Solving for variable 'w'.

Reorder the terms:
-12 + -5 + -18w + 12w2 = 5 + -5

Combine like terms: -12 + -5 = -17
-17 + -18w + 12w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-17 + -18w + 12w2 = 0

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

Divide each side by '12'.
-1.416666667 + -1.5w + w2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + -1.5w + 1.416666667 + w2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + -1.5w + w2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + -1.5w + w2 = 0 + 1.416666667
-1.5w + w2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
-1.5w + w2 = 1.416666667

The w term is -1.5w.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5w + 0.5625 + w2 = 1.416666667 + 0.5625

Reorder the terms:
0.5625 + -1.5w + w2 = 1.416666667 + 0.5625

Combine like terms: 1.416666667 + 0.5625 = 1.979166667
0.5625 + -1.5w + w2 = 1.979166667

Factor a perfect square on the left side:
(w + -0.75)(w + -0.75) = 1.979166667

Calculate the square root of the right side: 1.406828585

Break this problem into two subproblems by setting 
(w + -0.75) equal to 1.406828585 and -1.406828585.

Subproblem 1
w + -0.75 = 1.406828585

Simplifying
w + -0.75 = 1.406828585

Reorder the terms:
-0.75 + w = 1.406828585

Solving
-0.75 + w = 1.406828585

Solving for variable 'w'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + w = 1.406828585 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + w = 1.406828585 + 0.75
w = 1.406828585 + 0.75

Combine like terms: 1.406828585 + 0.75 = 2.156828585
w = 2.156828585

Simplifying
w = 2.156828585

Subproblem 2
w + -0.75 = -1.406828585

Simplifying
w + -0.75 = -1.406828585

Reorder the terms:
-0.75 + w = -1.406828585

Solving
-0.75 + w = -1.406828585

Solving for variable 'w'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + w = -1.406828585 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + w = -1.406828585 + 0.75
w = -1.406828585 + 0.75

Combine like terms: -1.406828585 + 0.75 = -0.656828585
w = -0.656828585

Simplifying
w = -0.656828585

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.156828585, -0.656828585}