3r^2-7r=6

Solution for 3r^2-7r=6 equation:

Simplifying
3r2 + -7r = 6

Reorder the terms:
-7r + 3r2 = 6

Solving
-7r + 3r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + -7r + 3r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -7r + 3r2 = 0

Factor a trinomial.
(-2 + -3r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve:

Simplifying
-2 + -3r = 0

Solving
-2 + -3r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3r = 0 + 2
-3r = 0 + 2

Combine like terms: 0 + 2 = 2
-3r = 2

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
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 = {-0.6666666667, 3}