2y^2(y^2-2)=18+y^2

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Solution for 2y^2(y^2-2)=18+y^2 equation: 


Simplifying
2y2(y2 + -2) = 18 + y2

Reorder the terms:
2y2(-2 + y2) = 18 + y2
(-2 * 2y2 + y2 * 2y2) = 18 + y2
(-4y2 + 2y4) = 18 + y2

Solving
-4y2 + 2y4 = 18 + y2

Solving for variable 'y'.

Reorder the terms:
-18 + -4y2 + -1y2 + 2y4 = 18 + y2 + -18 + -1y2

Combine like terms: -4y2 + -1y2 = -5y2
-18 + -5y2 + 2y4 = 18 + y2 + -18 + -1y2

Reorder the terms:
-18 + -5y2 + 2y4 = 18 + -18 + y2 + -1y2

Combine like terms: 18 + -18 = 0
-18 + -5y2 + 2y4 = 0 + y2 + -1y2
-18 + -5y2 + 2y4 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-18 + -5y2 + 2y4 = 0

Factor a trinomial.
(-2 + -1y2)(9 + -2y2) = 0


Subproblem 1
Set the factor '(-2 + -1y2)' equal to zero and attempt to solve:

Simplifying
-2 + -1y2 = 0

Solving
-2 + -1y2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y2 = 0 + 2
-1y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1y2 = 2

Divide each side by '-1'.
y2 = -2

Simplifying
y2 = -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 '(9 + -2y2)' equal to zero and attempt to solve:

Simplifying
9 + -2y2 = 0

Solving
9 + -2y2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2y2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2y2 = 0 + -9
-2y2 = 0 + -9

Combine like terms: 0 + -9 = -9
-2y2 = -9

Divide each side by '-2'.
y2 = 4.5

Simplifying
y2 = 4.5

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

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