(5r^2+3t^2)(5r^2-3t^2)=

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Solution for (5r^2+3t^2)(5r^2-3t^2)= equation: 


Simplifying
(5r2 + 3t2)(5r2 + -3t2) = 0

Multiply (5r2 + 3t2) * (5r2 + -3t2)
(5r2 * (5r2 + -3t2) + 3t2 * (5r2 + -3t2)) = 0
((5r2 * 5r2 + -3t2 * 5r2) + 3t2 * (5r2 + -3t2)) = 0

Reorder the terms:
((-15r2t2 + 25r4) + 3t2 * (5r2 + -3t2)) = 0
((-15r2t2 + 25r4) + 3t2 * (5r2 + -3t2)) = 0
(-15r2t2 + 25r4 + (5r2 * 3t2 + -3t2 * 3t2)) = 0
(-15r2t2 + 25r4 + (15r2t2 + -9t4)) = 0

Reorder the terms:
(-15r2t2 + 15r2t2 + 25r4 + -9t4) = 0

Combine like terms: -15r2t2 + 15r2t2 = 0
(0 + 25r4 + -9t4) = 0
(25r4 + -9t4) = 0

Solving
25r4 + -9t4 = 0

Solving for variable 'r'.

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

Add '9t4' to each side of the equation.
25r4 + -9t4 + 9t4 = 0 + 9t4

Combine like terms: -9t4 + 9t4 = 0
25r4 + 0 = 0 + 9t4
25r4 = 0 + 9t4
Remove the zero:
25r4 = 9t4

Divide each side by '25'.
r4 = 0.36t4

Simplifying
r4 = 0.36t4

Combine like terms: 0.36t4 + -0.36t4 = 0.00
r4 + -0.36t4 = 0.00

Factor a difference between two squares.
(r2 + 0.6t2)(r2 + -0.6t2) = 0.00


Subproblem 1
Set the factor '(r2 + 0.6t2)' equal to zero and attempt to solve:

Simplifying
r2 + 0.6t2 = 0

Solving
r2 + 0.6t2 = 0

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

Add '-0.6t2' to each side of the equation.
r2 + 0.6t2 + -0.6t2 = 0 + -0.6t2

Combine like terms: 0.6t2 + -0.6t2 = 0.0
r2 + 0.0 = 0 + -0.6t2
r2 = 0 + -0.6t2
Remove the zero:
r2 = -0.6t2

Simplifying
r2 = -0.6t2

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 '(r2 + -0.6t2)' equal to zero and attempt to solve:

Simplifying
r2 + -0.6t2 = 0

Solving
r2 + -0.6t2 = 0

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

Add '0.6t2' to each side of the equation.
r2 + -0.6t2 + 0.6t2 = 0 + 0.6t2

Combine like terms: -0.6t2 + 0.6t2 = 0.0
r2 + 0.0 = 0 + 0.6t2
r2 = 0 + 0.6t2
Remove the zero:
r2 = 0.6t2

Simplifying
r2 = 0.6t2

Take the square root of each side:
r = {-0.774596669t, 0.774596669t}
Solution
r = {-0.774596669t, 0.774596669t}

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