2(w-3)(w+7)-w(w+7)=96

Solution for 2(w-3)(w+7)-w(w+7)=96 equation:

Simplifying
2(w + -3)(w + 7) + -1w(w + 7) = 96

Reorder the terms:
2(-3 + w)(w + 7) + -1w(w + 7) = 96

Reorder the terms:
2(-3 + w)(7 + w) + -1w(w + 7) = 96

Multiply (-3 + w) * (7 + w)
2(-3(7 + w) + w(7 + w)) + -1w(w + 7) = 96
2((7 * -3 + w * -3) + w(7 + w)) + -1w(w + 7) = 96
2((-21 + -3w) + w(7 + w)) + -1w(w + 7) = 96
2(-21 + -3w + (7 * w + w * w)) + -1w(w + 7) = 96
2(-21 + -3w + (7w + w2)) + -1w(w + 7) = 96

Combine like terms: -3w + 7w = 4w
2(-21 + 4w + w2) + -1w(w + 7) = 96
(-21 * 2 + 4w * 2 + w2 * 2) + -1w(w + 7) = 96
(-42 + 8w + 2w2) + -1w(w + 7) = 96

Reorder the terms:
-42 + 8w + 2w2 + -1w(7 + w) = 96
-42 + 8w + 2w2 + (7 * -1w + w * -1w) = 96
-42 + 8w + 2w2 + (-7w + -1w2) = 96

Reorder the terms:
-42 + 8w + -7w + 2w2 + -1w2 = 96

Combine like terms: 8w + -7w = 1w
-42 + 1w + 2w2 + -1w2 = 96

Combine like terms: 2w2 + -1w2 = 1w2
-42 + 1w + 1w2 = 96

Solving
-42 + 1w + 1w2 = 96

Solving for variable 'w'.

Reorder the terms:
-42 + -96 + 1w + 1w2 = 96 + -96

Combine like terms: -42 + -96 = -138
-138 + 1w + 1w2 = 96 + -96

Combine like terms: 96 + -96 = 0
-138 + 1w + 1w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '138' to each side of the equation.
-138 + 1w + 138 + w2 = 0 + 138

Reorder the terms:
-138 + 138 + 1w + w2 = 0 + 138

Combine like terms: -138 + 138 = 0
0 + 1w + w2 = 0 + 138
1w + w2 = 0 + 138

Combine like terms: 0 + 138 = 138
1w + w2 = 138

The w term is 1w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
w + 0.25 + w2 = 138 + 0.25

Reorder the terms:
0.25 + w + w2 = 138 + 0.25

Combine like terms: 138 + 0.25 = 138.25
0.25 + w + w2 = 138.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 138.25

Calculate the square root of the right side: 11.757976016

Break this problem into two subproblems by setting 
(w + 0.5) equal to 11.757976016 and -11.757976016.

Subproblem 1
w + 0.5 = 11.757976016

Simplifying
w + 0.5 = 11.757976016

Reorder the terms:
0.5 + w = 11.757976016

Solving
0.5 + w = 11.757976016

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 11.757976016 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 11.757976016 + -0.5
w = 11.757976016 + -0.5

Combine like terms: 11.757976016 + -0.5 = 11.257976016
w = 11.257976016

Simplifying
w = 11.257976016

Subproblem 2
w + 0.5 = -11.757976016

Simplifying
w + 0.5 = -11.757976016

Reorder the terms:
0.5 + w = -11.757976016

Solving
0.5 + w = -11.757976016

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -11.757976016 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -11.757976016 + -0.5
w = -11.757976016 + -0.5

Combine like terms: -11.757976016 + -0.5 = -12.257976016
w = -12.257976016

Simplifying
w = -12.257976016

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {11.257976016, -12.257976016}