8w^3(6w^2-3)=

Solution for 8w^3(6w^2-3)= equation:

Simplifying
8w3(6w2 + -3) = 0

Reorder the terms:
8w3(-3 + 6w2) = 0
(-3 * 8w3 + 6w2 * 8w3) = 0
(-24w3 + 48w5) = 0

Solving
-24w3 + 48w5 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '24w3'.
24w3(-1 + 2w2) = 0

Ignore the factor 24.
Subproblem 1
Set the factor 'w3' equal to zero and attempt to solve:

Simplifying
w3 = 0

Solving
w3 = 0

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

Simplifying
w3 = 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 '(-1 + 2w2)' equal to zero and attempt to solve:

Simplifying
-1 + 2w2 = 0

Solving
-1 + 2w2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2w2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2w2 = 0 + 1
2w2 = 0 + 1

Combine like terms: 0 + 1 = 1
2w2 = 1

Divide each side by '2'.
w2 = 0.5

Simplifying
w2 = 0.5

Take the square root of each side:
w = {-0.707106781, 0.707106781}
Solution
w = {-0.707106781, 0.707106781}