R(R+1)=306

Solution for R(R+1)=306 equation:

Simplifying
R(R + 1) = 306

Reorder the terms:
R(1 + R) = 306
(1 * R + R * R) = 306
(1R + R2) = 306

Solving
1R + R2 = 306

Solving for variable 'R'.

Reorder the terms:
-306 + 1R + R2 = 306 + -306

Combine like terms: 306 + -306 = 0
-306 + 1R + R2 = 0

Factor a trinomial.
(-18 + -1R)(17 + -1R) = 0

Subproblem 1
Set the factor '(-18 + -1R)' equal to zero and attempt to solve:

Simplifying
-18 + -1R = 0

Solving
-18 + -1R = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1R = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1R = 0 + 18
-1R = 0 + 18

Combine like terms: 0 + 18 = 18
-1R = 18

Divide each side by '-1'.
R = -18

Simplifying
R = -18
Subproblem 2
Set the factor '(17 + -1R)' equal to zero and attempt to solve:

Simplifying
17 + -1R = 0

Solving
17 + -1R = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1R = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1R = 0 + -17
-1R = 0 + -17

Combine like terms: 0 + -17 = -17
-1R = -17

Divide each side by '-1'.
R = 17

Simplifying
R = 17
Solution
R = {-18, 17}