140=r(3r-1)

Solution for 140=r(3r-1) equation:

Simplifying
140 = r(3r + -1)

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

Solving
140 = -1r + 3r2

Solving for variable 'r'.

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {7, -6.666666667}