x^2=21x-90

Solution for x^2=21x-90 equation:

Simplifying
x2 = 21x + -90

Reorder the terms:
x2 = -90 + 21x

Solving
x2 = -90 + 21x

Solving for variable 'x'.

Reorder the terms:
90 + -21x + x2 = -90 + 21x + 90 + -21x

Reorder the terms:
90 + -21x + x2 = -90 + 90 + 21x + -21x

Combine like terms: -90 + 90 = 0
90 + -21x + x2 = 0 + 21x + -21x
90 + -21x + x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
90 + -21x + x2 = 0

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}