2r^2=9r+5

Solution for 2r^2=9r+5 equation:

Simplifying
2r2 = 9r + 5

Reorder the terms:
2r2 = 5 + 9r

Solving
2r2 = 5 + 9r

Solving for variable 'r'.

Reorder the terms:
-5 + -9r + 2r2 = 5 + 9r + -5 + -9r

Reorder the terms:
-5 + -9r + 2r2 = 5 + -5 + 9r + -9r

Combine like terms: 5 + -5 = 0
-5 + -9r + 2r2 = 0 + 9r + -9r
-5 + -9r + 2r2 = 9r + -9r

Combine like terms: 9r + -9r = 0
-5 + -9r + 2r2 = 0

Factor a trinomial.
(-1 + -2r)(5 + -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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.5, 5}