6(8+w)w=2(5-11w)

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Solution for 6(8+w)w=2(5-11w) equation: 


Simplifying
6(8 + w) * w = 2(5 + -11w)

Reorder the terms for easier multiplication:
6w(8 + w) = 2(5 + -11w)
(8 * 6w + w * 6w) = 2(5 + -11w)
(48w + 6w2) = 2(5 + -11w)
48w + 6w2 = (5 * 2 + -11w * 2)
48w + 6w2 = (10 + -22w)

Solving
48w + 6w2 = 10 + -22w

Solving for variable 'w'.

Reorder the terms:
-10 + 48w + 22w + 6w2 = 10 + -22w + -10 + 22w

Combine like terms: 48w + 22w = 70w
-10 + 70w + 6w2 = 10 + -22w + -10 + 22w

Reorder the terms:
-10 + 70w + 6w2 = 10 + -10 + -22w + 22w

Combine like terms: 10 + -10 = 0
-10 + 70w + 6w2 = 0 + -22w + 22w
-10 + 70w + 6w2 = -22w + 22w

Combine like terms: -22w + 22w = 0
-10 + 70w + 6w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 35w + 3w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 35w + 3w2)' equal to zero and attempt to solve:

Simplifying
-5 + 35w + 3w2 = 0

Solving
-5 + 35w + 3w2 = 0

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

Divide each side by '3'.
-1.666666667 + 11.66666667w + w2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 11.66666667w + 1.666666667 + w2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 11.66666667w + w2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 11.66666667w + w2 = 0 + 1.666666667
11.66666667w + w2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
11.66666667w + w2 = 1.666666667

The w term is 11.66666667w.  Take half its coefficient (5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
11.66666667w + 34.02777780 + w2 = 1.666666667 + 34.02777780

Reorder the terms:
34.02777780 + 11.66666667w + w2 = 1.666666667 + 34.02777780

Combine like terms: 1.666666667 + 34.02777780 = 35.694444467
34.02777780 + 11.66666667w + w2 = 35.694444467

Factor a perfect square on the left side:
(w + 5.833333335)(w + 5.833333335) = 35.694444467

Calculate the square root of the right side: 5.974482778

Break this problem into two subproblems by setting 
(w + 5.833333335) equal to 5.974482778 and -5.974482778.


Subproblem 1
w + 5.833333335 = 5.974482778

Simplifying
w + 5.833333335 = 5.974482778

Reorder the terms:
5.833333335 + w = 5.974482778

Solving
5.833333335 + w = 5.974482778

Solving for variable 'w'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + w = 5.974482778 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + w = 5.974482778 + -5.833333335
w = 5.974482778 + -5.833333335

Combine like terms: 5.974482778 + -5.833333335 = 0.141149443
w = 0.141149443

Simplifying
w = 0.141149443


Subproblem 2
w + 5.833333335 = -5.974482778

Simplifying
w + 5.833333335 = -5.974482778

Reorder the terms:
5.833333335 + w = -5.974482778

Solving
5.833333335 + w = -5.974482778

Solving for variable 'w'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + w = -5.974482778 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + w = -5.974482778 + -5.833333335
w = -5.974482778 + -5.833333335

Combine like terms: -5.974482778 + -5.833333335 = -11.807816113
w = -11.807816113

Simplifying
w = -11.807816113


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.141149443, -11.807816113}
Solution
w = {0.141149443, -11.807816113}

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