2r^2+3r=5

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

Simplifying
2r2 + 3r = 5

Reorder the terms:
3r + 2r2 = 5

Solving
3r + 2r2 = 5

Solving for variable 'r'.

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

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

Factor a trinomial.
(-5 + -2r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-5 + -2r)' equal to zero and attempt to solve:

Simplifying
-5 + -2r = 0

Solving
-5 + -2r = 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 + -2r = 0 + 5

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

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

Divide each side by '-2'.
r = -2.5

Simplifying
r = -2.5
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

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

Simplifying
r = 1
Solution
r = {-2.5, 1}