10(w-4)=4(w+4)4w

Solution for 10(w-4)=4(w+4)4w equation:

Simplifying
10(w + -4) = 4(w + 4) * 4w

Reorder the terms:
10(-4 + w) = 4(w + 4) * 4w
(-4 * 10 + w * 10) = 4(w + 4) * 4w
(-40 + 10w) = 4(w + 4) * 4w

Reorder the terms:
-40 + 10w = 4(4 + w) * 4w

Reorder the terms for easier multiplication:
-40 + 10w = 4 * 4w(4 + w)

Multiply 4 * 4
-40 + 10w = 16w(4 + w)
-40 + 10w = (4 * 16w + w * 16w)
-40 + 10w = (64w + 16w2)

Solving
-40 + 10w = 64w + 16w2

Solving for variable 'w'.

Combine like terms: 10w + -64w = -54w
-40 + -54w + -16w2 = 64w + 16w2 + -64w + -16w2

Reorder the terms:
-40 + -54w + -16w2 = 64w + -64w + 16w2 + -16w2

Combine like terms: 64w + -64w = 0
-40 + -54w + -16w2 = 0 + 16w2 + -16w2
-40 + -54w + -16w2 = 16w2 + -16w2

Combine like terms: 16w2 + -16w2 = 0
-40 + -54w + -16w2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(20 + 27w + 8w2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(20 + 27w + 8w2)' equal to zero and attempt to solve:

Simplifying
20 + 27w + 8w2 = 0

Solving
20 + 27w + 8w2 = 0

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

Divide each side by '8'.
2.5 + 3.375w + w2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 3.375w + -2.5 + w2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 3.375w + w2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 3.375w + w2 = 0 + -2.5
3.375w + w2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
3.375w + w2 = -2.5

The w term is 3.375w.  Take half its coefficient (1.6875).
Square it (2.84765625) and add it to both sides.

Add '2.84765625' to each side of the equation.
3.375w + 2.84765625 + w2 = -2.5 + 2.84765625

Reorder the terms:
2.84765625 + 3.375w + w2 = -2.5 + 2.84765625

Combine like terms: -2.5 + 2.84765625 = 0.34765625
2.84765625 + 3.375w + w2 = 0.34765625

Factor a perfect square on the left side:
(w + 1.6875)(w + 1.6875) = 0.34765625

Calculate the square root of the right side: 0.589623821

Break this problem into two subproblems by setting 
(w + 1.6875) equal to 0.589623821 and -0.589623821.

Subproblem 1
w + 1.6875 = 0.589623821

Simplifying
w + 1.6875 = 0.589623821

Reorder the terms:
1.6875 + w = 0.589623821

Solving
1.6875 + w = 0.589623821

Solving for variable 'w'.

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

Add '-1.6875' to each side of the equation.
1.6875 + -1.6875 + w = 0.589623821 + -1.6875

Combine like terms: 1.6875 + -1.6875 = 0.0000
0.0000 + w = 0.589623821 + -1.6875
w = 0.589623821 + -1.6875

Combine like terms: 0.589623821 + -1.6875 = -1.097876179
w = -1.097876179

Simplifying
w = -1.097876179

Subproblem 2
w + 1.6875 = -0.589623821

Simplifying
w + 1.6875 = -0.589623821

Reorder the terms:
1.6875 + w = -0.589623821

Solving
1.6875 + w = -0.589623821

Solving for variable 'w'.

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

Add '-1.6875' to each side of the equation.
1.6875 + -1.6875 + w = -0.589623821 + -1.6875

Combine like terms: 1.6875 + -1.6875 = 0.0000
0.0000 + w = -0.589623821 + -1.6875
w = -0.589623821 + -1.6875

Combine like terms: -0.589623821 + -1.6875 = -2.277123821
w = -2.277123821

Simplifying
w = -2.277123821

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.097876179, -2.277123821}
Solution
w = {-1.097876179, -2.277123821}