25r-25r^2-6=0

Solution for 25r-25r^2-6=0 equation:

Simplifying
25r + -25r2 + -6 = 0

Reorder the terms:
-6 + 25r + -25r2 = 0

Solving
-6 + 25r + -25r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-3 + 5r)' equal to zero and attempt to solve:

Simplifying
-3 + 5r = 0

Solving
-3 + 5r = 0

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

Add '3' to each side of the equation.
-3 + 3 + 5r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5r = 0 + 3
5r = 0 + 3

Combine like terms: 0 + 3 = 3
5r = 3

Divide each side by '5'.
r = 0.6

Simplifying
r = 0.6
Subproblem 2
Set the factor '(2 + -5r)' equal to zero and attempt to solve:

Simplifying
2 + -5r = 0

Solving
2 + -5r = 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 + -5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5r = 0 + -2
-5r = 0 + -2

Combine like terms: 0 + -2 = -2
-5r = -2

Divide each side by '-5'.
r = 0.4

Simplifying
r = 0.4
Solution
r = {0.6, 0.4}