5r^2+3r=8

Solution for 5r^2+3r=8 equation:

Simplifying
5r2 + 3r = 8

Reorder the terms:
3r + 5r2 = 8

Solving
3r + 5r2 = 8

Solving for variable 'r'.

Reorder the terms:
-8 + 3r + 5r2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 3r + 5r2 = 0

Factor a trinomial.
(-8 + -5r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-8 + -5r)' equal to zero and attempt to solve:

Simplifying
-8 + -5r = 0

Solving
-8 + -5r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5r = 0 + 8
-5r = 0 + 8

Combine like terms: 0 + 8 = 8
-5r = 8

Divide each side by '-5'.
r = -1.6

Simplifying
r = -1.6
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 = {-1.6, 1}