(5x^2-13)(5x^2-13)=0

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Solution for (5x^2-13)(5x^2-13)=0 equation: 


Simplifying
(5x2 + -13)(5x2 + -13) = 0

Reorder the terms:
(-13 + 5x2)(5x2 + -13) = 0

Reorder the terms:
(-13 + 5x2)(-13 + 5x2) = 0

Multiply (-13 + 5x2) * (-13 + 5x2)
(-13(-13 + 5x2) + 5x2 * (-13 + 5x2)) = 0
((-13 * -13 + 5x2 * -13) + 5x2 * (-13 + 5x2)) = 0
((169 + -65x2) + 5x2 * (-13 + 5x2)) = 0
(169 + -65x2 + (-13 * 5x2 + 5x2 * 5x2)) = 0
(169 + -65x2 + (-65x2 + 25x4)) = 0

Combine like terms: -65x2 + -65x2 = -130x2
(169 + -130x2 + 25x4) = 0

Solving
169 + -130x2 + 25x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -5x2)(13 + -5x2) = 0


Subproblem 1
Set the factor '(13 + -5x2)' equal to zero and attempt to solve:

Simplifying
13 + -5x2 = 0

Solving
13 + -5x2 = 0

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

Add '-13' to each side of the equation.
13 + -13 + -5x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5x2 = 0 + -13
-5x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-5x2 = -13

Divide each side by '-5'.
x2 = 2.6

Simplifying
x2 = 2.6

Take the square root of each side:
x = {-1.61245155, 1.61245155}

Subproblem 2
Set the factor '(13 + -5x2)' equal to zero and attempt to solve:

Simplifying
13 + -5x2 = 0

Solving
13 + -5x2 = 0

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

Add '-13' to each side of the equation.
13 + -13 + -5x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5x2 = 0 + -13
-5x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-5x2 = -13

Divide each side by '-5'.
x2 = 2.6

Simplifying
x2 = 2.6

Take the square root of each side:
x = {-1.61245155, 1.61245155}
Solution
x = {-1.61245155, 1.61245155, -1.61245155, 1.61245155}

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