(x^2)(x^2-61)=192

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Solution for (x^2)(x^2-61)=192 equation: 


Simplifying
(x2)(x2 + -61) = 192

Reorder the terms:
x2(-61 + x2) = 192
(-61 * x2 + x2 * x2) = 192
(-61x2 + x4) = 192

Solving
-61x2 + x4 = 192

Solving for variable 'x'.

Reorder the terms:
-192 + -61x2 + x4 = 192 + -192

Combine like terms: 192 + -192 = 0
-192 + -61x2 + x4 = 0

Factor a trinomial.
(-3 + -1x2)(64 + -1x2) = 0

Factor a difference between two squares.
(-3 + -1x2)((8 + x)(8 + -1x)) = 0


Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
x2 = -3

Simplifying
x2 = -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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-8, 8}

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