2w^2(w^2-3)=27-3w^2

Solution for 2w^2(w^2-3)=27-3w^2 equation:

Simplifying
2w2(w2 + -3) = 27 + -3w2

Reorder the terms:
2w2(-3 + w2) = 27 + -3w2
(-3 * 2w2 + w2 * 2w2) = 27 + -3w2
(-6w2 + 2w4) = 27 + -3w2

Solving
-6w2 + 2w4 = 27 + -3w2

Solving for variable 'w'.

Reorder the terms:
-27 + -6w2 + 3w2 + 2w4 = 27 + -3w2 + -27 + 3w2

Combine like terms: -6w2 + 3w2 = -3w2
-27 + -3w2 + 2w4 = 27 + -3w2 + -27 + 3w2

Reorder the terms:
-27 + -3w2 + 2w4 = 27 + -27 + -3w2 + 3w2

Combine like terms: 27 + -27 = 0
-27 + -3w2 + 2w4 = 0 + -3w2 + 3w2
-27 + -3w2 + 2w4 = -3w2 + 3w2

Combine like terms: -3w2 + 3w2 = 0
-27 + -3w2 + 2w4 = 0

Factor a trinomial.
(-3 + -1w2)(9 + -2w2) = 0

Subproblem 1
Set the factor '(-3 + -1w2)' equal to zero and attempt to solve:

Simplifying
-3 + -1w2 = 0

Solving
-3 + -1w2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w2 = 0 + 3
-1w2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1w2 = 3

Divide each side by '-1'.
w2 = -3

Simplifying
w2 = -3

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 '(9 + -2w2)' equal to zero and attempt to solve:

Simplifying
9 + -2w2 = 0

Solving
9 + -2w2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2w2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2w2 = 0 + -9
-2w2 = 0 + -9

Combine like terms: 0 + -9 = -9
-2w2 = -9

Divide each side by '-2'.
w2 = 4.5

Simplifying
w2 = 4.5

Take the square root of each side:
w = {-2.121320344, 2.121320344}
Solution
w = {-2.121320344, 2.121320344}