10r^2-53r+36=0

Solution for 10r^2-53r+36=0 equation:

Simplifying
10r2 + -53r + 36 = 0

Reorder the terms:
36 + -53r + 10r2 = 0

Solving
36 + -53r + 10r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4 + -5r)(9 + -2r) = 0

Subproblem 1
Set the factor '(4 + -5r)' equal to zero and attempt to solve:

Simplifying
4 + -5r = 0

Solving
4 + -5r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5r = 0 + -4
-5r = 0 + -4

Combine like terms: 0 + -4 = -4
-5r = -4

Divide each side by '-5'.
r = 0.8

Simplifying
r = 0.8
Subproblem 2
Set the factor '(9 + -2r)' equal to zero and attempt to solve:

Simplifying
9 + -2r = 0

Solving
9 + -2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2r = 0 + -9
-2r = 0 + -9

Combine like terms: 0 + -9 = -9
-2r = -9

Divide each side by '-2'.
r = 4.5

Simplifying
r = 4.5
Solution
r = {0.8, 4.5}