16=x^2(17-x^2)

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Solution for 16=x^2(17-x^2) equation: 


Simplifying
16 = x2(17 + -1x2)
16 = (17 * x2 + -1x2 * x2)
16 = (17x2 + -1x4)

Solving
16 = 17x2 + -1x4

Solving for variable 'x'.

Reorder the terms:
16 + -17x2 + x4 = 17x2 + -17x2 + -1x4 + x4

Combine like terms: 17x2 + -17x2 = 0
16 + -17x2 + x4 = 0 + -1x4 + x4
16 + -17x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
16 + -17x2 + x4 = 0

Factor a trinomial.
(1 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(16 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(1 + x)(1 + -1x) = 0


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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 1, -4, 4}

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