x^2=24x-63

Solution for x^2=24x-63 equation:

Simplifying
x2 = 24x + -63

Reorder the terms:
x2 = -63 + 24x

Solving
x2 = -63 + 24x

Solving for variable 'x'.

Reorder the terms:
63 + -24x + x2 = -63 + 24x + 63 + -24x

Reorder the terms:
63 + -24x + x2 = -63 + 63 + 24x + -24x

Combine like terms: -63 + 63 = 0
63 + -24x + x2 = 0 + 24x + -24x
63 + -24x + x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
63 + -24x + x2 = 0

Factor a trinomial.
(3 + -1x)(21 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {3, 21}