x^2=21x-110

Solution for x^2=21x-110 equation:

Simplifying
x2 = 21x + -110

Reorder the terms:
x2 = -110 + 21x

Solving
x2 = -110 + 21x

Solving for variable 'x'.

Reorder the terms:
110 + -21x + x2 = -110 + 21x + 110 + -21x

Reorder the terms:
110 + -21x + x2 = -110 + 110 + 21x + -21x

Combine like terms: -110 + 110 = 0
110 + -21x + x2 = 0 + 21x + -21x
110 + -21x + x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
110 + -21x + x2 = 0

Factor a trinomial.
(10 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
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 = {10, 11}