3r+115=4r^2

Solution for 3r+115=4r^2 equation:

Simplifying
3r + 115 = 4r2

Reorder the terms:
115 + 3r = 4r2

Solving
115 + 3r = 4r2

Solving for variable 'r'.

Combine like terms: 4r2 + -4r2 = 0
115 + 3r + -4r2 = 0

Factor a trinomial.
(23 + -4r)(5 + r) = 0

Subproblem 1
Set the factor '(23 + -4r)' equal to zero and attempt to solve:

Simplifying
23 + -4r = 0

Solving
23 + -4r = 0

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

Add '-23' to each side of the equation.
23 + -23 + -4r = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -4r = 0 + -23
-4r = 0 + -23

Combine like terms: 0 + -23 = -23
-4r = -23

Divide each side by '-4'.
r = 5.75

Simplifying
r = 5.75
Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

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

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

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

Simplifying
r = -5
Solution
r = {5.75, -5}