(x^2-9)(x^2-16)-15x^2=0

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Solution for (x^2-9)(x^2-16)-15x^2=0 equation: 


Simplifying
(x2 + -9)(x2 + -16) + -15x2 = 0

Reorder the terms:
(-9 + x2)(x2 + -16) + -15x2 = 0

Reorder the terms:
(-9 + x2)(-16 + x2) + -15x2 = 0

Multiply (-9 + x2) * (-16 + x2)
(-9(-16 + x2) + x2(-16 + x2)) + -15x2 = 0
((-16 * -9 + x2 * -9) + x2(-16 + x2)) + -15x2 = 0
((144 + -9x2) + x2(-16 + x2)) + -15x2 = 0
(144 + -9x2 + (-16 * x2 + x2 * x2)) + -15x2 = 0
(144 + -9x2 + (-16x2 + x4)) + -15x2 = 0

Combine like terms: -9x2 + -16x2 = -25x2
(144 + -25x2 + x4) + -15x2 = 0

Reorder the terms:
144 + -25x2 + -15x2 + x4 = 0

Combine like terms: -25x2 + -15x2 = -40x2
144 + -40x2 + x4 = 0

Solving
144 + -40x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(36 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(36 + -1x2) = 0

Factor a difference between two squares.
((6 + x)(6 + -1x))(2 + x)(2 + -1x) = 0


Subproblem 1
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 2
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

Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

Subproblem 4
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 2, -6, 6}

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