(r^2-5t^2)(r^2-2t^2)=

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


Simplifying
(r2 + -5t2)(r2 + -2t2) = 0

Multiply (r2 + -5t2) * (r2 + -2t2)
(r2(r2 + -2t2) + -5t2 * (r2 + -2t2)) = 0
((r2 * r2 + -2t2 * r2) + -5t2 * (r2 + -2t2)) = 0

Reorder the terms:
((-2r2t2 + r4) + -5t2 * (r2 + -2t2)) = 0
((-2r2t2 + r4) + -5t2 * (r2 + -2t2)) = 0
(-2r2t2 + r4 + (r2 * -5t2 + -2t2 * -5t2)) = 0
(-2r2t2 + r4 + (-5r2t2 + 10t4)) = 0

Reorder the terms:
(-2r2t2 + -5r2t2 + r4 + 10t4) = 0

Combine like terms: -2r2t2 + -5r2t2 = -7r2t2
(-7r2t2 + r4 + 10t4) = 0

Solving
-7r2t2 + r4 + 10t4 = 0

Solving for variable 'r'.

Factor a trinomial.
(r2 + -5t2)(r2 + -2t2) = 0


Subproblem 1
Set the factor '(r2 + -5t2)' equal to zero and attempt to solve:

Simplifying
r2 + -5t2 = 0

Solving
r2 + -5t2 = 0

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

Add '5t2' to each side of the equation.
r2 + -5t2 + 5t2 = 0 + 5t2

Combine like terms: -5t2 + 5t2 = 0
r2 + 0 = 0 + 5t2
r2 = 0 + 5t2
Remove the zero:
r2 = 5t2

Simplifying
r2 = 5t2

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

Subproblem 2
Set the factor '(r2 + -2t2)' equal to zero and attempt to solve:

Simplifying
r2 + -2t2 = 0

Solving
r2 + -2t2 = 0

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

Add '2t2' to each side of the equation.
r2 + -2t2 + 2t2 = 0 + 2t2

Combine like terms: -2t2 + 2t2 = 0
r2 + 0 = 0 + 2t2
r2 = 0 + 2t2
Remove the zero:
r2 = 2t2

Simplifying
r2 = 2t2

Take the square root of each side:
r = {-1.414213562t, 1.414213562t}
Solution
r = {-2.236067978t, 2.236067978t, -1.414213562t, 1.414213562t}

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