r(2r+1)=78

Solution for r(2r+1)=78 equation:

Simplifying
r(2r + 1) = 78

Reorder the terms:
r(1 + 2r) = 78
(1 * r + 2r * r) = 78
(1r + 2r2) = 78

Solving
1r + 2r2 = 78

Solving for variable 'r'.

Reorder the terms:
-78 + 1r + 2r2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 1r + 2r2 = 0

Factor a trinomial.
(-13 + -2r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-13 + -2r)' equal to zero and attempt to solve:

Simplifying
-13 + -2r = 0

Solving
-13 + -2r = 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 + -2r = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2r = 0 + 13
-2r = 0 + 13

Combine like terms: 0 + 13 = 13
-2r = 13

Divide each side by '-2'.
r = -6.5

Simplifying
r = -6.5
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 = {-6.5, 6}