x^2-16x+83=20

Solution for x^2-16x+83=20 equation:

Simplifying
x2 + -16x + 83 = 20

Reorder the terms:
83 + -16x + x2 = 20

Solving
83 + -16x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
83 + -20 + -16x + x2 = 20 + -20

Combine like terms: 83 + -20 = 63
63 + -16x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
63 + -16x + x2 = 0

Factor a trinomial.
(7 + -1x)(9 + -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 '(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 = {7, 9}