c^2+14c-51=0

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

Simplifying
c2 + 14c + -51 = 0

Reorder the terms:
-51 + 14c + c2 = 0

Solving
-51 + 14c + c2 = 0

Solving for variable 'c'.

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

Subproblem 1
Set the factor '(-17 + -1c)' equal to zero and attempt to solve:

Simplifying
-17 + -1c = 0

Solving
-17 + -1c = 0

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

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

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

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

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

Simplifying
c = -17
Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

Solving
3 + -1c = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1c = 0 + -3
-1c = 0 + -3

Combine like terms: 0 + -3 = -3
-1c = -3

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {-17, 3}