(z+5)(z+5)=81

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

Simplifying
(z + 5)(z + 5) = 81

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

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

Multiply (5 + z) * (5 + z)
(5(5 + z) + z(5 + z)) = 81
((5 * 5 + z * 5) + z(5 + z)) = 81
((25 + 5z) + z(5 + z)) = 81
(25 + 5z + (5 * z + z * z)) = 81
(25 + 5z + (5z + z2)) = 81

Combine like terms: 5z + 5z = 10z
(25 + 10z + z2) = 81

Solving
25 + 10z + z2 = 81

Solving for variable 'z'.

Reorder the terms:
25 + -81 + 10z + z2 = 81 + -81

Combine like terms: 25 + -81 = -56
-56 + 10z + z2 = 81 + -81

Combine like terms: 81 + -81 = 0
-56 + 10z + z2 = 0

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

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

Simplifying
-14 + -1z = 0

Solving
-14 + -1z = 0

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

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

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

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

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

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

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

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

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

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

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

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