5r^2=11r+12

Solution for 5r^2=11r+12 equation:

Simplifying
5r2 = 11r + 12

Reorder the terms:
5r2 = 12 + 11r

Solving
5r2 = 12 + 11r

Solving for variable 'r'.

Reorder the terms:
-12 + -11r + 5r2 = 12 + 11r + -12 + -11r

Reorder the terms:
-12 + -11r + 5r2 = 12 + -12 + 11r + -11r

Combine like terms: 12 + -12 = 0
-12 + -11r + 5r2 = 0 + 11r + -11r
-12 + -11r + 5r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
-12 + -11r + 5r2 = 0

Factor a trinomial.
(-4 + -5r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -5r)' equal to zero and attempt to solve:

Simplifying
-4 + -5r = 0

Solving
-4 + -5r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5r = 0 + 4
-5r = 0 + 4

Combine like terms: 0 + 4 = 4
-5r = 4

Divide each side by '-5'.
r = -0.8

Simplifying
r = -0.8
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 = {-0.8, 3}