w^2(-4w^2-2)+(-5w^2)(-2w^2-2)=

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Solution for w^2(-4w^2-2)+(-5w^2)(-2w^2-2)= equation: 


Simplifying
w2(-4w2 + -2) + (-5w2)(-2w2 + -2) = 0

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

Remove parenthesis around (-5w2)
-2w2 + -4w4 + -5w2(-2w2 + -2) = 0

Reorder the terms:
-2w2 + -4w4 + -5w2(-2 + -2w2) = 0
-2w2 + -4w4 + (-2 * -5w2 + -2w2 * -5w2) = 0
-2w2 + -4w4 + (10w2 + 10w4) = 0

Reorder the terms:
-2w2 + 10w2 + -4w4 + 10w4 = 0

Combine like terms: -2w2 + 10w2 = 8w2
8w2 + -4w4 + 10w4 = 0

Combine like terms: -4w4 + 10w4 = 6w4
8w2 + 6w4 = 0

Solving
8w2 + 6w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w2'.
2w2(4 + 3w2) = 0

Ignore the factor 2.

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 '(4 + 3w2)' equal to zero and attempt to solve:

Simplifying
4 + 3w2 = 0

Solving
4 + 3w2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3w2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3w2 = 0 + -4
3w2 = 0 + -4

Combine like terms: 0 + -4 = -4
3w2 = -4

Divide each side by '3'.
w2 = -1.333333333

Simplifying
w2 = -1.333333333

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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