9x^4=40x^2-16

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Solution for 9x^4=40x^2-16 equation: 


Simplifying
9x4 = 40x2 + -16

Reorder the terms:
9x4 = -16 + 40x2

Solving
9x4 = -16 + 40x2

Solving for variable 'x'.

Reorder the terms:
16 + -40x2 + 9x4 = -16 + 40x2 + 16 + -40x2

Reorder the terms:
16 + -40x2 + 9x4 = -16 + 16 + 40x2 + -40x2

Combine like terms: -16 + 16 = 0
16 + -40x2 + 9x4 = 0 + 40x2 + -40x2
16 + -40x2 + 9x4 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
16 + -40x2 + 9x4 = 0

Factor a trinomial.
(4 + -9x2)(4 + -1x2) = 0

Factor a difference between two squares.
((2 + 3x)(2 + -3x))(4 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(2 + 3x)(2 + -3x) = 0


Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 4
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

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

Simplifying
x = 2
Solution
x = {-0.6666666667, 0.6666666667, -2, 2}

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