3r^2-r=140

Solution for 3r^2-r=140 equation:

Simplifying
3r2 + -1r = 140

Reorder the terms:
-1r + 3r2 = 140

Solving
-1r + 3r2 = 140

Solving for variable 'r'.

Reorder the terms:
-140 + -1r + 3r2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + -1r + 3r2 = 0

Factor a trinomial.
(-20 + -3r)(7 + -1r) = 0

Subproblem 1
Set the factor '(-20 + -3r)' equal to zero and attempt to solve:

Simplifying
-20 + -3r = 0

Solving
-20 + -3r = 0

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

Add '20' to each side of the equation.
-20 + 20 + -3r = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3r = 0 + 20
-3r = 0 + 20

Combine like terms: 0 + 20 = 20
-3r = 20

Divide each side by '-3'.
r = -6.666666667

Simplifying
r = -6.666666667
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-6.666666667, 7}