0=x^2+14x-51

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

Simplifying
0 = x2 + 14x + -51

Reorder the terms:
0 = -51 + 14x + x2

Solving
0 = -51 + 14x + x2

Solving for variable 'x'.

Combine like terms: 0 + 51 = 51
51 + -14x + -1x2 = -51 + 14x + x2 + 51 + -14x + -1x2

Reorder the terms:
51 + -14x + -1x2 = -51 + 51 + 14x + -14x + x2 + -1x2

Combine like terms: -51 + 51 = 0
51 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
51 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
51 + -14x + -1x2 = 0 + x2 + -1x2
51 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
51 + -14x + -1x2 = 0

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

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

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

Simplifying
17 + x = 0

Solving
17 + x = 0

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

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

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

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