6r^2+7r=13

Solution for 6r^2+7r=13 equation:

Simplifying
6r2 + 7r = 13

Reorder the terms:
7r + 6r2 = 13

Solving
7r + 6r2 = 13

Solving for variable 'r'.

Reorder the terms:
-13 + 7r + 6r2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 7r + 6r2 = 0

Factor a trinomial.
(-13 + -6r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-13 + -6r)' equal to zero and attempt to solve:

Simplifying
-13 + -6r = 0

Solving
-13 + -6r = 0

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

Add '13' to each side of the equation.
-13 + 13 + -6r = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6r = 0 + 13
-6r = 0 + 13

Combine like terms: 0 + 13 = 13
-6r = 13

Divide each side by '-6'.
r = -2.166666667

Simplifying
r = -2.166666667
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {-2.166666667, 1}