3r^2-4r=84

Solution for 3r^2-4r=84 equation:

Simplifying
3r2 + -4r = 84

Reorder the terms:
-4r + 3r2 = 84

Solving
-4r + 3r2 = 84

Solving for variable 'r'.

Reorder the terms:
-84 + -4r + 3r2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -4r + 3r2 = 0

Factor a trinomial.
(-14 + -3r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-14 + -3r)' equal to zero and attempt to solve:

Simplifying
-14 + -3r = 0

Solving
-14 + -3r = 0

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

Add '14' to each side of the equation.
-14 + 14 + -3r = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -3r = 0 + 14
-3r = 0 + 14

Combine like terms: 0 + 14 = 14
-3r = 14

Divide each side by '-3'.
r = -4.666666667

Simplifying
r = -4.666666667
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-4.666666667, 6}