(z+2)(z+2)=9

Solution for (z+2)(z+2)=9 equation:

Simplifying
(z + 2)(z + 2) = 9

Reorder the terms:
(2 + z)(z + 2) = 9

Reorder the terms:
(2 + z)(2 + z) = 9

Multiply (2 + z) * (2 + z)
(2(2 + z) + z(2 + z)) = 9
((2 * 2 + z * 2) + z(2 + z)) = 9
((4 + 2z) + z(2 + z)) = 9
(4 + 2z + (2 * z + z * z)) = 9
(4 + 2z + (2z + z2)) = 9

Combine like terms: 2z + 2z = 4z
(4 + 4z + z2) = 9

Solving
4 + 4z + z2 = 9

Solving for variable 'z'.

Reorder the terms:
4 + -9 + 4z + z2 = 9 + -9

Combine like terms: 4 + -9 = -5
-5 + 4z + z2 = 9 + -9

Combine like terms: 9 + -9 = 0
-5 + 4z + z2 = 0

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

Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 0

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

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

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

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

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Solution
z = {-5, 1}