(5x^2-25)(2x^2-36)=0

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Solution for (5x^2-25)(2x^2-36)=0 equation: 


Simplifying
(5x2 + -25)(2x2 + -36) = 0

Reorder the terms:
(-25 + 5x2)(2x2 + -36) = 0

Reorder the terms:
(-25 + 5x2)(-36 + 2x2) = 0

Multiply (-25 + 5x2) * (-36 + 2x2)
(-25(-36 + 2x2) + 5x2 * (-36 + 2x2)) = 0
((-36 * -25 + 2x2 * -25) + 5x2 * (-36 + 2x2)) = 0
((900 + -50x2) + 5x2 * (-36 + 2x2)) = 0
(900 + -50x2 + (-36 * 5x2 + 2x2 * 5x2)) = 0
(900 + -50x2 + (-180x2 + 10x4)) = 0

Combine like terms: -50x2 + -180x2 = -230x2
(900 + -230x2 + 10x4) = 0

Solving
900 + -230x2 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(90 + -23x2 + x4) = 0

Factor a trinomial.
10((5 + -1x2)(18 + -1x2)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

Subproblem 2
Set the factor '(18 + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -1x2 = 0

Solving
18 + -1x2 = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x2 = 0 + -18
-1x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-1x2 = -18

Divide each side by '-1'.
x2 = 18

Simplifying
x2 = 18

Take the square root of each side:
x = {-4.242640687, 4.242640687}
Solution
x = {-2.236067978, 2.236067978, -4.242640687, 4.242640687}

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