2r^2=5r+3

Solution for 2r^2=5r+3 equation:

Simplifying
2r2 = 5r + 3

Reorder the terms:
2r2 = 3 + 5r

Solving
2r2 = 3 + 5r

Solving for variable 'r'.

Reorder the terms:
-3 + -5r + 2r2 = 3 + 5r + -3 + -5r

Reorder the terms:
-3 + -5r + 2r2 = 3 + -3 + 5r + -5r

Combine like terms: 3 + -3 = 0
-3 + -5r + 2r2 = 0 + 5r + -5r
-3 + -5r + 2r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
-3 + -5r + 2r2 = 0

Factor a trinomial.
(-1 + -2r)(3 + -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 '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.5, 3}