7w(-3)(4w+8)=11

Solution for 7w(-3)(4w+8)=11 equation:

Simplifying
7w(-3)(4w + 8) = 11

Reorder the terms:
7w * -3(8 + 4w) = 11

Reorder the terms for easier multiplication:
7 * -3w(8 + 4w) = 11

Multiply 7 * -3
-21w(8 + 4w) = 11
(8 * -21w + 4w * -21w) = 11
(-168w + -84w2) = 11

Solving
-168w + -84w2 = 11

Solving for variable 'w'.

Reorder the terms:
-11 + -168w + -84w2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -168w + -84w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 168w + 84w2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + 168w + 84w2)' equal to zero and attempt to solve:

Simplifying
11 + 168w + 84w2 = 0

Solving
11 + 168w + 84w2 = 0

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

Divide each side by '84'.
0.130952381 + 2w + w2 = 0

Move the constant term to the right:

Add '-0.130952381' to each side of the equation.
0.130952381 + 2w + -0.130952381 + w2 = 0 + -0.130952381

Reorder the terms:
0.130952381 + -0.130952381 + 2w + w2 = 0 + -0.130952381

Combine like terms: 0.130952381 + -0.130952381 = 0.000000000
0.000000000 + 2w + w2 = 0 + -0.130952381
2w + w2 = 0 + -0.130952381

Combine like terms: 0 + -0.130952381 = -0.130952381
2w + w2 = -0.130952381

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = -0.130952381 + 1

Reorder the terms:
1 + 2w + w2 = -0.130952381 + 1

Combine like terms: -0.130952381 + 1 = 0.869047619
1 + 2w + w2 = 0.869047619

Factor a perfect square on the left side:
(w + 1)(w + 1) = 0.869047619

Calculate the square root of the right side: 0.932227236

Break this problem into two subproblems by setting 
(w + 1) equal to 0.932227236 and -0.932227236.

Subproblem 1
w + 1 = 0.932227236

Simplifying
w + 1 = 0.932227236

Reorder the terms:
1 + w = 0.932227236

Solving
1 + w = 0.932227236

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 0.932227236 + -1

Combine like terms: 1 + -1 = 0
0 + w = 0.932227236 + -1
w = 0.932227236 + -1

Combine like terms: 0.932227236 + -1 = -0.067772764
w = -0.067772764

Simplifying
w = -0.067772764

Subproblem 2
w + 1 = -0.932227236

Simplifying
w + 1 = -0.932227236

Reorder the terms:
1 + w = -0.932227236

Solving
1 + w = -0.932227236

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -0.932227236 + -1

Combine like terms: 1 + -1 = 0
0 + w = -0.932227236 + -1
w = -0.932227236 + -1

Combine like terms: -0.932227236 + -1 = -1.932227236
w = -1.932227236

Simplifying
w = -1.932227236

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.067772764, -1.932227236}
Solution
w = {-0.067772764, -1.932227236}