2(r^2+1)-5r=0

Solution for 2(r^2+1)-5r=0 equation:

Simplifying
2(r2 + 1) + -5r = 0

Reorder the terms:
2(1 + r2) + -5r = 0
(1 * 2 + r2 * 2) + -5r = 0
(2 + 2r2) + -5r = 0

Reorder the terms:
2 + -5r + 2r2 = 0

Solving
2 + -5r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -2r)(2 + -1r) = 0

Subproblem 1
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0.5, 2}