15r^2-16rt+4t^2=

Solution for 15r^2-16rt+4t^2= equation:

Simplifying
15r2 + -16rt + 4t2 = 0

Reorder the terms:
-16rt + 15r2 + 4t2 = 0

Solving
-16rt + 15r2 + 4t2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3r + -2t)(5r + -2t) = 0

Subproblem 1
Set the factor '(3r + -2t)' equal to zero and attempt to solve:

Simplifying
3r + -2t = 0

Solving
3r + -2t = 0

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

Add '2t' to each side of the equation.
3r + -2t + 2t = 0 + 2t

Combine like terms: -2t + 2t = 0
3r + 0 = 0 + 2t
3r = 0 + 2t
Remove the zero:
3r = 2t

Divide each side by '3'.
r = 0.6666666667t

Simplifying
r = 0.6666666667t
Subproblem 2
Set the factor '(5r + -2t)' equal to zero and attempt to solve:

Simplifying
5r + -2t = 0

Solving
5r + -2t = 0

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

Add '2t' to each side of the equation.
5r + -2t + 2t = 0 + 2t

Combine like terms: -2t + 2t = 0
5r + 0 = 0 + 2t
5r = 0 + 2t
Remove the zero:
5r = 2t

Divide each side by '5'.
r = 0.4t

Simplifying
r = 0.4t
Solution
r = {0.6666666667t, 0.4t}