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

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

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

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

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

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

Combine like terms: -2w + 3w = 1w
(-3 + 1w + 2w2) = 5

Solving
-3 + 1w + 2w2 = 5

Solving for variable 'w'.

Reorder the terms:
-3 + -5 + 1w + 2w2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + 1w + 2w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + 1w + 2w2 = 0

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

Divide each side by '2'.
-4 + 0.5w + w2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.5w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.5w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.5w + w2 = 0 + 4
0.5w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.5w + w2 = 4

The w term is 0.5w.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5w + 0.0625 + w2 = 4 + 0.0625

Reorder the terms:
0.0625 + 0.5w + w2 = 4 + 0.0625

Combine like terms: 4 + 0.0625 = 4.0625
0.0625 + 0.5w + w2 = 4.0625

Factor a perfect square on the left side:
(w + 0.25)(w + 0.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(w + 0.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
w + 0.25 = 2.015564437

Simplifying
w + 0.25 = 2.015564437

Reorder the terms:
0.25 + w = 2.015564437

Solving
0.25 + w = 2.015564437

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = 2.015564437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = 2.015564437 + -0.25
w = 2.015564437 + -0.25

Combine like terms: 2.015564437 + -0.25 = 1.765564437
w = 1.765564437

Simplifying
w = 1.765564437

Subproblem 2
w + 0.25 = -2.015564437

Simplifying
w + 0.25 = -2.015564437

Reorder the terms:
0.25 + w = -2.015564437

Solving
0.25 + w = -2.015564437

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = -2.015564437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = -2.015564437 + -0.25
w = -2.015564437 + -0.25

Combine like terms: -2.015564437 + -0.25 = -2.265564437
w = -2.265564437

Simplifying
w = -2.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.765564437, -2.265564437}