9x^2(x^2-2)=7x^2-16

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Solution for 9x^2(x^2-2)=7x^2-16 equation: 


Simplifying
9x2(x2 + -2) = 7x2 + -16

Reorder the terms:
9x2(-2 + x2) = 7x2 + -16
(-2 * 9x2 + x2 * 9x2) = 7x2 + -16
(-18x2 + 9x4) = 7x2 + -16

Reorder the terms:
-18x2 + 9x4 = -16 + 7x2

Solving
-18x2 + 9x4 = -16 + 7x2

Solving for variable 'x'.

Reorder the terms:
16 + -18x2 + -7x2 + 9x4 = -16 + 7x2 + 16 + -7x2

Combine like terms: -18x2 + -7x2 = -25x2
16 + -25x2 + 9x4 = -16 + 7x2 + 16 + -7x2

Reorder the terms:
16 + -25x2 + 9x4 = -16 + 16 + 7x2 + -7x2

Combine like terms: -16 + 16 = 0
16 + -25x2 + 9x4 = 0 + 7x2 + -7x2
16 + -25x2 + 9x4 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
16 + -25x2 + 9x4 = 0

Factor a trinomial.
(1 + -1x2)(16 + -9x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(16 + -9x2) = 0

Factor a difference between two squares.
((4 + 3x)(4 + -3x))(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 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-1, 1, -1.333333333, 1.333333333}

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