x^2-21x+100=80

Solution for x^2-21x+100=80 equation:

Simplifying
x2 + -21x + 100 = 80

Reorder the terms:
100 + -21x + x2 = 80

Solving
100 + -21x + x2 = 80

Solving for variable 'x'.

Reorder the terms:
100 + -80 + -21x + x2 = 80 + -80

Combine like terms: 100 + -80 = 20
20 + -21x + x2 = 80 + -80

Combine like terms: 80 + -80 = 0
20 + -21x + x2 = 0

Factor a trinomial.
(1 + -1x)(20 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {1, 20}