25r^2-33r+9=-3r

Solution for 25r^2-33r+9=-3r equation:

Simplifying
25r2 + -33r + 9 = -3r

Reorder the terms:
9 + -33r + 25r2 = -3r

Solving
9 + -33r + 25r2 = -3r

Solving for variable 'r'.

Reorder the terms:
9 + -33r + 3r + 25r2 = -3r + 3r

Combine like terms: -33r + 3r = -30r
9 + -30r + 25r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
9 + -30r + 25r2 = 0

Factor a trinomial.
(3 + -5r)(3 + -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 '(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
Solution
r = {0.6, 0.6}