(x^2-7)(5x^2-3)=0

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Solution for (x^2-7)(5x^2-3)=0 equation: 


Simplifying
(x2 + -7)(5x2 + -3) = 0

Reorder the terms:
(-7 + x2)(5x2 + -3) = 0

Reorder the terms:
(-7 + x2)(-3 + 5x2) = 0

Multiply (-7 + x2) * (-3 + 5x2)
(-7(-3 + 5x2) + x2(-3 + 5x2)) = 0
((-3 * -7 + 5x2 * -7) + x2(-3 + 5x2)) = 0
((21 + -35x2) + x2(-3 + 5x2)) = 0
(21 + -35x2 + (-3 * x2 + 5x2 * x2)) = 0
(21 + -35x2 + (-3x2 + 5x4)) = 0

Combine like terms: -35x2 + -3x2 = -38x2
(21 + -38x2 + 5x4) = 0

Solving
21 + -38x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -5x2)(7 + -1x2) = 0


Subproblem 1
Set the factor '(3 + -5x2)' equal to zero and attempt to solve:

Simplifying
3 + -5x2 = 0

Solving
3 + -5x2 = 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 + -5x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x2 = 0 + -3
-5x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5x2 = -3

Divide each side by '-5'.
x2 = 0.6

Simplifying
x2 = 0.6

Take the square root of each side:
x = {-0.774596669, 0.774596669}

Subproblem 2
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Solution
x = {-0.774596669, 0.774596669, -2.645751311, 2.645751311}

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