2w^3(2w^3-7w-1)+w(5w^3+2w)=

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Solution for 2w^3(2w^3-7w-1)+w(5w^3+2w)= equation: 


Simplifying
2w3(2w3 + -7w + -1) + w(5w3 + 2w) = 0

Reorder the terms:
2w3(-1 + -7w + 2w3) + w(5w3 + 2w) = 0
(-1 * 2w3 + -7w * 2w3 + 2w3 * 2w3) + w(5w3 + 2w) = 0
(-2w3 + -14w4 + 4w6) + w(5w3 + 2w) = 0

Reorder the terms:
-2w3 + -14w4 + 4w6 + w(2w + 5w3) = 0
-2w3 + -14w4 + 4w6 + (2w * w + 5w3 * w) = 0
-2w3 + -14w4 + 4w6 + (2w2 + 5w4) = 0

Reorder the terms:
2w2 + -2w3 + -14w4 + 5w4 + 4w6 = 0

Combine like terms: -14w4 + 5w4 = -9w4
2w2 + -2w3 + -9w4 + 4w6 = 0

Solving
2w2 + -2w3 + -9w4 + 4w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w2'.
w2(2 + -2w + -9w2 + 4w4) = 0


Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve:

Simplifying
w2 = 0

Solving
w2 = 0

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

Simplifying
w2 = 0

Take the square root of each side:
w = {0}

Subproblem 2
Set the factor '(2 + -2w + -9w2 + 4w4)' equal to zero and attempt to solve:

Simplifying
2 + -2w + -9w2 + 4w4 = 0

Solving
2 + -2w + -9w2 + 4w4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
w = {0}

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