(a+3)(a+3)=64

Solution for (a+3)(a+3)=64 equation:

Simplifying
(a + 3)(a + 3) = 64

Reorder the terms:
(3 + a)(a + 3) = 64

Reorder the terms:
(3 + a)(3 + a) = 64

Multiply (3 + a) * (3 + a)
(3(3 + a) + a(3 + a)) = 64
((3 * 3 + a * 3) + a(3 + a)) = 64
((9 + 3a) + a(3 + a)) = 64
(9 + 3a + (3 * a + a * a)) = 64
(9 + 3a + (3a + a2)) = 64

Combine like terms: 3a + 3a = 6a
(9 + 6a + a2) = 64

Solving
9 + 6a + a2 = 64

Solving for variable 'a'.

Reorder the terms:
9 + -64 + 6a + a2 = 64 + -64

Combine like terms: 9 + -64 = -55
-55 + 6a + a2 = 64 + -64

Combine like terms: 64 + -64 = 0
-55 + 6a + a2 = 0

Factor a trinomial.
(-11 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-11 + -1a)' equal to zero and attempt to solve:

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-11, 5}