X^2-21X+90=0

Solution for X^2-21X+90=0 equation:

Simplifying
X2 + -21X + 90 = 0

Reorder the terms:
90 + -21X + X2 = 0

Solving
90 + -21X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(6 + -1X)(15 + -1X) = 0

Subproblem 1
Set the factor '(6 + -1X)' equal to zero and attempt to solve:

Simplifying
6 + -1X = 0

Solving
6 + -1X = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1X = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X = 0 + -6
-1X = 0 + -6

Combine like terms: 0 + -6 = -6
-1X = -6

Divide each side by '-1'.
X = 6

Simplifying
X = 6
Subproblem 2
Set the factor '(15 + -1X)' equal to zero and attempt to solve:

Simplifying
15 + -1X = 0

Solving
15 + -1X = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1X = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1X = 0 + -15
-1X = 0 + -15

Combine like terms: 0 + -15 = -15
-1X = -15

Divide each side by '-1'.
X = 15

Simplifying
X = 15
Solution
X = {6, 15}