a(a+3)=a+63

Solution for a(a+3)=a+63 equation:

Simplifying
a(a + 3) = a + 63

Reorder the terms:
a(3 + a) = a + 63
(3 * a + a * a) = a + 63
(3a + a2) = a + 63

Reorder the terms:
3a + a2 = 63 + a

Solving
3a + a2 = 63 + a

Solving for variable 'a'.

Reorder the terms:
-63 + 3a + -1a + a2 = 63 + a + -63 + -1a

Combine like terms: 3a + -1a = 2a
-63 + 2a + a2 = 63 + a + -63 + -1a

Reorder the terms:
-63 + 2a + a2 = 63 + -63 + a + -1a

Combine like terms: 63 + -63 = 0
-63 + 2a + a2 = 0 + a + -1a
-63 + 2a + a2 = a + -1a

Combine like terms: a + -1a = 0
-63 + 2a + a2 = 0

Factor a trinomial.
(-9 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-9, 7}