3w^2(w^2+3)=8+7w^2

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Solution for 3w^2(w^2+3)=8+7w^2 equation: 


Simplifying
3w2(w2 + 3) = 8 + 7w2

Reorder the terms:
3w2(3 + w2) = 8 + 7w2
(3 * 3w2 + w2 * 3w2) = 8 + 7w2
(9w2 + 3w4) = 8 + 7w2

Solving
9w2 + 3w4 = 8 + 7w2

Solving for variable 'w'.

Reorder the terms:
-8 + 9w2 + -7w2 + 3w4 = 8 + 7w2 + -8 + -7w2

Combine like terms: 9w2 + -7w2 = 2w2
-8 + 2w2 + 3w4 = 8 + 7w2 + -8 + -7w2

Reorder the terms:
-8 + 2w2 + 3w4 = 8 + -8 + 7w2 + -7w2

Combine like terms: 8 + -8 = 0
-8 + 2w2 + 3w4 = 0 + 7w2 + -7w2
-8 + 2w2 + 3w4 = 7w2 + -7w2

Combine like terms: 7w2 + -7w2 = 0
-8 + 2w2 + 3w4 = 0

Factor a trinomial.
(-2 + -1w2)(4 + -3w2) = 0


Subproblem 1
Set the factor '(-2 + -1w2)' equal to zero and attempt to solve:

Simplifying
-2 + -1w2 = 0

Solving
-2 + -1w2 = 0

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

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

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

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

Divide each side by '-1'.
w2 = -2

Simplifying
w2 = -2

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 '(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

Take the square root of each side:
w = {-1.154700538, 1.154700538}
Solution
w = {-1.154700538, 1.154700538}

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