(16x^2-9)(x^2-4)=0

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Solution for (16x^2-9)(x^2-4)=0 equation:


Simplifying
(16x2 + -9)(x2 + -4) = 0

Reorder the terms:
(-9 + 16x2)(x2 + -4) = 0

Reorder the terms:
(-9 + 16x2)(-4 + x2) = 0

Multiply (-9 + 16x2) * (-4 + x2)
(-9(-4 + x2) + 16x2 * (-4 + x2)) = 0
((-4 * -9 + x2 * -9) + 16x2 * (-4 + x2)) = 0
((36 + -9x2) + 16x2 * (-4 + x2)) = 0
(36 + -9x2 + (-4 * 16x2 + x2 * 16x2)) = 0
(36 + -9x2 + (-64x2 + 16x4)) = 0

Combine like terms: -9x2 + -64x2 = -73x2
(36 + -73x2 + 16x4) = 0

Solving
36 + -73x2 + 16x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -16x2)(4 + -1x2) = 0

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

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


Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

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

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

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

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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 = {-0.75, 0.75, -2, 2}

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