(r^2+5)(r^2-2)=0

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Solution for (r^2+5)(r^2-2)=0 equation: 


Simplifying
(r2 + 5)(r2 + -2) = 0

Reorder the terms:
(5 + r2)(r2 + -2) = 0

Reorder the terms:
(5 + r2)(-2 + r2) = 0

Multiply (5 + r2) * (-2 + r2)
(5(-2 + r2) + r2(-2 + r2)) = 0
((-2 * 5 + r2 * 5) + r2(-2 + r2)) = 0
((-10 + 5r2) + r2(-2 + r2)) = 0
(-10 + 5r2 + (-2 * r2 + r2 * r2)) = 0
(-10 + 5r2 + (-2r2 + r4)) = 0

Combine like terms: 5r2 + -2r2 = 3r2
(-10 + 3r2 + r4) = 0

Solving
-10 + 3r2 + r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -1r2)(2 + -1r2) = 0


Subproblem 1
Set the factor '(-5 + -1r2)' equal to zero and attempt to solve:

Simplifying
-5 + -1r2 = 0

Solving
-5 + -1r2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r2 = 0 + 5
-1r2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1r2 = 5

Divide each side by '-1'.
r2 = -5

Simplifying
r2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + -1r2)' equal to zero and attempt to solve:

Simplifying
2 + -1r2 = 0

Solving
2 + -1r2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r2 = 0 + -2
-1r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1r2 = -2

Divide each side by '-1'.
r2 = 2

Simplifying
r2 = 2

Take the square root of each side:
r = {-1.414213562, 1.414213562}
Solution
r = {-1.414213562, 1.414213562}

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