x^2-14x+51=6

Solution for x^2-14x+51=6 equation:

Simplifying
x2 + -14x + 51 = 6

Reorder the terms:
51 + -14x + x2 = 6

Solving
51 + -14x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
51 + -6 + -14x + x2 = 6 + -6

Combine like terms: 51 + -6 = 45
45 + -14x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
45 + -14x + x2 = 0

Factor a trinomial.
(5 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {5, 9}