8w(2w-1)-4w=80

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Solution for 8w(2w-1)-4w=80 equation: 


Simplifying
8w(2w + -1) + -4w = 80

Reorder the terms:
8w(-1 + 2w) + -4w = 80
(-1 * 8w + 2w * 8w) + -4w = 80
(-8w + 16w2) + -4w = 80

Reorder the terms:
-8w + -4w + 16w2 = 80

Combine like terms: -8w + -4w = -12w
-12w + 16w2 = 80

Solving
-12w + 16w2 = 80

Solving for variable 'w'.

Reorder the terms:
-80 + -12w + 16w2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + -12w + 16w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + -3w + 4w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + -3w + 4w2)' equal to zero and attempt to solve:

Simplifying
-20 + -3w + 4w2 = 0

Solving
-20 + -3w + 4w2 = 0

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

Divide each side by '4'.
-5 + -0.75w + w2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.75w + 5 + w2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.75w + w2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.75w + w2 = 0 + 5
-0.75w + w2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.75w + w2 = 5

The w term is -0.75w.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75w + 0.140625 + w2 = 5 + 0.140625

Reorder the terms:
0.140625 + -0.75w + w2 = 5 + 0.140625

Combine like terms: 5 + 0.140625 = 5.140625
0.140625 + -0.75w + w2 = 5.140625

Factor a perfect square on the left side:
(w + -0.375)(w + -0.375) = 5.140625

Calculate the square root of the right side: 2.267294643

Break this problem into two subproblems by setting 
(w + -0.375) equal to 2.267294643 and -2.267294643.


Subproblem 1
w + -0.375 = 2.267294643

Simplifying
w + -0.375 = 2.267294643

Reorder the terms:
-0.375 + w = 2.267294643

Solving
-0.375 + w = 2.267294643

Solving for variable 'w'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + w = 2.267294643 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + w = 2.267294643 + 0.375
w = 2.267294643 + 0.375

Combine like terms: 2.267294643 + 0.375 = 2.642294643
w = 2.642294643

Simplifying
w = 2.642294643


Subproblem 2
w + -0.375 = -2.267294643

Simplifying
w + -0.375 = -2.267294643

Reorder the terms:
-0.375 + w = -2.267294643

Solving
-0.375 + w = -2.267294643

Solving for variable 'w'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + w = -2.267294643 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + w = -2.267294643 + 0.375
w = -2.267294643 + 0.375

Combine like terms: -2.267294643 + 0.375 = -1.892294643
w = -1.892294643

Simplifying
w = -1.892294643


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.642294643, -1.892294643}
Solution
w = {2.642294643, -1.892294643}

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