5W^2(W^2+3)=54-6W^2

Solution for 5W^2(W^2+3)=54-6W^2 equation:

Simplifying
5W2(W2 + 3) = 54 + -6W2

Reorder the terms:
5W2(3 + W2) = 54 + -6W2
(3 * 5W2 + W2 * 5W2) = 54 + -6W2
(15W2 + 5W4) = 54 + -6W2

Solving
15W2 + 5W4 = 54 + -6W2

Solving for variable 'W'.

Reorder the terms:
-54 + 15W2 + 6W2 + 5W4 = 54 + -6W2 + -54 + 6W2

Combine like terms: 15W2 + 6W2 = 21W2
-54 + 21W2 + 5W4 = 54 + -6W2 + -54 + 6W2

Reorder the terms:
-54 + 21W2 + 5W4 = 54 + -54 + -6W2 + 6W2

Combine like terms: 54 + -54 = 0
-54 + 21W2 + 5W4 = 0 + -6W2 + 6W2
-54 + 21W2 + 5W4 = -6W2 + 6W2

Combine like terms: -6W2 + 6W2 = 0
-54 + 21W2 + 5W4 = 0

Factor a trinomial.
(-6 + -1W2)(9 + -5W2) = 0

Subproblem 1
Set the factor '(-6 + -1W2)' equal to zero and attempt to solve:

Simplifying
-6 + -1W2 = 0

Solving
-6 + -1W2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1W2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1W2 = 0 + 6
-1W2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1W2 = 6

Divide each side by '-1'.
W2 = -6

Simplifying
W2 = -6

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 + -5W2)' equal to zero and attempt to solve:

Simplifying
9 + -5W2 = 0

Solving
9 + -5W2 = 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 + -5W2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5W2 = 0 + -9
-5W2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5W2 = -9

Divide each side by '-5'.
W2 = 1.8

Simplifying
W2 = 1.8

Take the square root of each side:
W = {-1.341640787, 1.341640787}
Solution
W = {-1.341640787, 1.341640787}