5r^2-3=2r

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

Simplifying
5r2 + -3 = 2r

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

Solving
-3 + 5r2 = 2r

Solving for variable 'r'.

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

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

Factor a trinomial.
(-3 + -5r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -5r)' equal to zero and attempt to solve:

Simplifying
-3 + -5r = 0

Solving
-3 + -5r = 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 + -5r = 0 + 3

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

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

Divide each side by '-5'.
r = -0.6

Simplifying
r = -0.6
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 = {-0.6, 1}