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

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

Simplifying
(5r + 2t)(5r + -2t) = 0

Multiply (5r + 2t) * (5r + -2t)
(5r * (5r + -2t) + 2t * (5r + -2t)) = 0
((5r * 5r + -2t * 5r) + 2t * (5r + -2t)) = 0

Reorder the terms:
((-10rt + 25r2) + 2t * (5r + -2t)) = 0
((-10rt + 25r2) + 2t * (5r + -2t)) = 0
(-10rt + 25r2 + (5r * 2t + -2t * 2t)) = 0
(-10rt + 25r2 + (10rt + -4t2)) = 0

Reorder the terms:
(-10rt + 10rt + 25r2 + -4t2) = 0

Combine like terms: -10rt + 10rt = 0
(0 + 25r2 + -4t2) = 0
(25r2 + -4t2) = 0

Solving
25r2 + -4t2 = 0

Solving for variable 'r'.

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

Add '4t2' to each side of the equation.
25r2 + -4t2 + 4t2 = 0 + 4t2

Combine like terms: -4t2 + 4t2 = 0
25r2 + 0 = 0 + 4t2
25r2 = 0 + 4t2
Remove the zero:
25r2 = 4t2

Divide each side by '25'.
r2 = 0.16t2

Simplifying
r2 = 0.16t2

Take the square root of each side:
r = {-0.4t, 0.4t}