a^2=24a-63

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

Simplifying
a2 = 24a + -63

Reorder the terms:
a2 = -63 + 24a

Solving
a2 = -63 + 24a

Solving for variable 'a'.

Reorder the terms:
63 + -24a + a2 = -63 + 24a + 63 + -24a

Reorder the terms:
63 + -24a + a2 = -63 + 63 + 24a + -24a

Combine like terms: -63 + 63 = 0
63 + -24a + a2 = 0 + 24a + -24a
63 + -24a + a2 = 24a + -24a

Combine like terms: 24a + -24a = 0
63 + -24a + a2 = 0

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

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

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

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

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

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

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

Simplifying
21 + -1a = 0

Solving
21 + -1a = 0

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

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

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

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

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

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