(v+2)(v+2)=9

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

Simplifying
(v + 2)(v + 2) = 9

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

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

Multiply (2 + v) * (2 + v)
(2(2 + v) + v(2 + v)) = 9
((2 * 2 + v * 2) + v(2 + v)) = 9
((4 + 2v) + v(2 + v)) = 9
(4 + 2v + (2 * v + v * v)) = 9
(4 + 2v + (2v + v2)) = 9

Combine like terms: 2v + 2v = 4v
(4 + 4v + v2) = 9

Solving
4 + 4v + v2 = 9

Solving for variable 'v'.

Reorder the terms:
4 + -9 + 4v + v2 = 9 + -9

Combine like terms: 4 + -9 = -5
-5 + 4v + v2 = 9 + -9

Combine like terms: 9 + -9 = 0
-5 + 4v + v2 = 0

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

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

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

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

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

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

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

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

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