r^2+14r-51=0

Solution for r^2+14r-51=0 equation:

Simplifying
r2 + 14r + -51 = 0

Reorder the terms:
-51 + 14r + r2 = 0

Solving
-51 + 14r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-17 + -1r)(3 + -1r) = 0

Subproblem 1
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
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 = {-17, 3}