(4x^2-9)(x^2-10)=0

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Solution for (4x^2-9)(x^2-10)=0 equation: 


Simplifying
(4x2 + -9)(x2 + -10) = 0

Reorder the terms:
(-9 + 4x2)(x2 + -10) = 0

Reorder the terms:
(-9 + 4x2)(-10 + x2) = 0

Multiply (-9 + 4x2) * (-10 + x2)
(-9(-10 + x2) + 4x2 * (-10 + x2)) = 0
((-10 * -9 + x2 * -9) + 4x2 * (-10 + x2)) = 0
((90 + -9x2) + 4x2 * (-10 + x2)) = 0
(90 + -9x2 + (-10 * 4x2 + x2 * 4x2)) = 0
(90 + -9x2 + (-40x2 + 4x4)) = 0

Combine like terms: -9x2 + -40x2 = -49x2
(90 + -49x2 + 4x4) = 0

Solving
90 + -49x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -4x2)(10 + -1x2) = 0

Factor a difference between two squares.
((3 + 2x)(3 + -2x))(10 + -1x2) = 0


Subproblem 1
Set the factor '(10 + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -1x2 = 0

Solving
10 + -1x2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x2 = 0 + -10
-1x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1x2 = -10

Divide each side by '-1'.
x2 = 10

Simplifying
x2 = 10

Take the square root of each side:
x = {-3.16227766, 3.16227766}

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-3.16227766, 3.16227766, -1.5, 1.5}

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