(a+5)(a+5)=81

Solution for (a+5)(a+5)=81 equation:

Simplifying
(a + 5)(a + 5) = 81

Reorder the terms:
(5 + a)(a + 5) = 81

Reorder the terms:
(5 + a)(5 + a) = 81

Multiply (5 + a) * (5 + a)
(5(5 + a) + a(5 + a)) = 81
((5 * 5 + a * 5) + a(5 + a)) = 81
((25 + 5a) + a(5 + a)) = 81
(25 + 5a + (5 * a + a * a)) = 81
(25 + 5a + (5a + a2)) = 81

Combine like terms: 5a + 5a = 10a
(25 + 10a + a2) = 81

Solving
25 + 10a + a2 = 81

Solving for variable 'a'.

Reorder the terms:
25 + -81 + 10a + a2 = 81 + -81

Combine like terms: 25 + -81 = -56
-56 + 10a + a2 = 81 + -81

Combine like terms: 81 + -81 = 0
-56 + 10a + a2 = 0

Factor a trinomial.
(-14 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-14 + -1a)' equal to zero and attempt to solve:

Simplifying
-14 + -1a = 0

Solving
-14 + -1a = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1a = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1a = 0 + 14
-1a = 0 + 14

Combine like terms: 0 + 14 = 14
-1a = 14

Divide each side by '-1'.
a = -14

Simplifying
a = -14
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-14, 4}