3r^2-11r=130

Solution for 3r^2-11r=130 equation:

Simplifying
3r2 + -11r = 130

Reorder the terms:
-11r + 3r2 = 130

Solving
-11r + 3r2 = 130

Solving for variable 'r'.

Reorder the terms:
-130 + -11r + 3r2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + -11r + 3r2 = 0

Factor a trinomial.
(-5 + -1r)(26 + -3r) = 0

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 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 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(26 + -3r)' equal to zero and attempt to solve:

Simplifying
26 + -3r = 0

Solving
26 + -3r = 0

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

Add '-26' to each side of the equation.
26 + -26 + -3r = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -3r = 0 + -26
-3r = 0 + -26

Combine like terms: 0 + -26 = -26
-3r = -26

Divide each side by '-3'.
r = 8.666666667

Simplifying
r = 8.666666667
Solution
r = {-5, 8.666666667}