x^2-18x+83=6

Solution for x^2-18x+83=6 equation:

Simplifying
x2 + -18x + 83 = 6

Reorder the terms:
83 + -18x + x2 = 6

Solving
83 + -18x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
83 + -6 + -18x + x2 = 6 + -6

Combine like terms: 83 + -6 = 77
77 + -18x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
77 + -18x + x2 = 0

Factor a trinomial.
(7 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {7, 11}