-8w^4(-4+4w+75w^2+3w-13)=

Solution for -8w^4(-4+4w+75w^2+3w-13)= equation:

Simplifying
-8w4(-4 + 4w + 75w2 + 3w + -13) = 0

Reorder the terms:
-8w4(-4 + -13 + 4w + 3w + 75w2) = 0

Combine like terms: -4 + -13 = -17
-8w4(-17 + 4w + 3w + 75w2) = 0

Combine like terms: 4w + 3w = 7w
-8w4(-17 + 7w + 75w2) = 0
(-17 * -8w4 + 7w * -8w4 + 75w2 * -8w4) = 0
(136w4 + -56w5 + -600w6) = 0

Solving
136w4 + -56w5 + -600w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '8w4'.
8w4(17 + -7w + -75w2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve:

Simplifying
w4 = 0

Solving
w4 = 0

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

Simplifying
w4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(17 + -7w + -75w2)' equal to zero and attempt to solve:

Simplifying
17 + -7w + -75w2 = 0

Solving
17 + -7w + -75w2 = 0

Begin completing the square.  Divide all terms by
-75 the coefficient of the squared term: 

Divide each side by '-75'.
-0.2266666667 + 0.09333333333w + w2 = 0

Move the constant term to the right:

Add '0.2266666667' to each side of the equation.
-0.2266666667 + 0.09333333333w + 0.2266666667 + w2 = 0 + 0.2266666667

Reorder the terms:
-0.2266666667 + 0.2266666667 + 0.09333333333w + w2 = 0 + 0.2266666667

Combine like terms: -0.2266666667 + 0.2266666667 = 0.0000000000
0.0000000000 + 0.09333333333w + w2 = 0 + 0.2266666667
0.09333333333w + w2 = 0 + 0.2266666667

Combine like terms: 0 + 0.2266666667 = 0.2266666667
0.09333333333w + w2 = 0.2266666667

The w term is 0.09333333333w.  Take half its coefficient (0.04666666667).
Square it (0.002177777778) and add it to both sides.

Add '0.002177777778' to each side of the equation.
0.09333333333w + 0.002177777778 + w2 = 0.2266666667 + 0.002177777778

Reorder the terms:
0.002177777778 + 0.09333333333w + w2 = 0.2266666667 + 0.002177777778

Combine like terms: 0.2266666667 + 0.002177777778 = 0.228844444478
0.002177777778 + 0.09333333333w + w2 = 0.228844444478

Factor a perfect square on the left side:
(w + 0.04666666667)(w + 0.04666666667) = 0.228844444478

Calculate the square root of the right side: 0.478376885

Break this problem into two subproblems by setting 
(w + 0.04666666667) equal to 0.478376885 and -0.478376885.

Subproblem 1
w + 0.04666666667 = 0.478376885

Simplifying
w + 0.04666666667 = 0.478376885

Reorder the terms:
0.04666666667 + w = 0.478376885

Solving
0.04666666667 + w = 0.478376885

Solving for variable 'w'.

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

Add '-0.04666666667' to each side of the equation.
0.04666666667 + -0.04666666667 + w = 0.478376885 + -0.04666666667

Combine like terms: 0.04666666667 + -0.04666666667 = 0.00000000000
0.00000000000 + w = 0.478376885 + -0.04666666667
w = 0.478376885 + -0.04666666667

Combine like terms: 0.478376885 + -0.04666666667 = 0.43171021833
w = 0.43171021833

Simplifying
w = 0.43171021833

Subproblem 2
w + 0.04666666667 = -0.478376885

Simplifying
w + 0.04666666667 = -0.478376885

Reorder the terms:
0.04666666667 + w = -0.478376885

Solving
0.04666666667 + w = -0.478376885

Solving for variable 'w'.

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

Add '-0.04666666667' to each side of the equation.
0.04666666667 + -0.04666666667 + w = -0.478376885 + -0.04666666667

Combine like terms: 0.04666666667 + -0.04666666667 = 0.00000000000
0.00000000000 + w = -0.478376885 + -0.04666666667
w = -0.478376885 + -0.04666666667

Combine like terms: -0.478376885 + -0.04666666667 = -0.52504355167
w = -0.52504355167

Simplifying
w = -0.52504355167

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.43171021833, -0.52504355167}
Solution
w = {0.43171021833, -0.52504355167}