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

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


Simplifying
(x2 + -7)(5 + -1x2) = 0

Reorder the terms:
(-7 + x2)(5 + -1x2) = 0

Multiply (-7 + x2) * (5 + -1x2)
(-7(5 + -1x2) + x2(5 + -1x2)) = 0
((5 * -7 + -1x2 * -7) + x2(5 + -1x2)) = 0
((-35 + 7x2) + x2(5 + -1x2)) = 0
(-35 + 7x2 + (5 * x2 + -1x2 * x2)) = 0
(-35 + 7x2 + (5x2 + -1x4)) = 0

Combine like terms: 7x2 + 5x2 = 12x2
(-35 + 12x2 + -1x4) = 0

Solving
-35 + 12x2 + -1x4 = 0

Solving for variable 'x'.

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


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

Simplifying
-7 + x2 = 0

Solving
-7 + x2 = 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 + x2 = 0 + 7

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

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

Simplifying
x2 = 7

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

Subproblem 2
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}
Solution
x = {-2.645751311, 2.645751311, -2.236067978, 2.236067978}

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