(3+2*a)(3+2*a)=121

Solution for (3+2*a)(3+2*a)=121 equation:

Simplifying
(3 + 2a)(3 + 2a) = 121

Multiply (3 + 2a) * (3 + 2a)
(3(3 + 2a) + 2a * (3 + 2a)) = 121
((3 * 3 + 2a * 3) + 2a * (3 + 2a)) = 121
((9 + 6a) + 2a * (3 + 2a)) = 121
(9 + 6a + (3 * 2a + 2a * 2a)) = 121
(9 + 6a + (6a + 4a2)) = 121

Combine like terms: 6a + 6a = 12a
(9 + 12a + 4a2) = 121

Solving
9 + 12a + 4a2 = 121

Solving for variable 'a'.

Reorder the terms:
9 + -121 + 12a + 4a2 = 121 + -121

Combine like terms: 9 + -121 = -112
-112 + 12a + 4a2 = 121 + -121

Combine like terms: 121 + -121 = 0
-112 + 12a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + 3a + a2) = 0

Factor a trinomial.
4((-7 + -1a)(4 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
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 = {-7, 4}