(a+1)(a+2)=12

Solution for (a+1)(a+2)=12 equation:

Simplifying
(a + 1)(a + 2) = 12

Reorder the terms:
(1 + a)(a + 2) = 12

Reorder the terms:
(1 + a)(2 + a) = 12

Multiply (1 + a) * (2 + a)
(1(2 + a) + a(2 + a)) = 12
((2 * 1 + a * 1) + a(2 + a)) = 12
((2 + 1a) + a(2 + a)) = 12
(2 + 1a + (2 * a + a * a)) = 12
(2 + 1a + (2a + a2)) = 12

Combine like terms: 1a + 2a = 3a
(2 + 3a + a2) = 12

Solving
2 + 3a + a2 = 12

Solving for variable 'a'.

Reorder the terms:
2 + -12 + 3a + a2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 3a + a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 3a + a2 = 0

Factor a trinomial.
(-5 + -1a)(2 + -1a) = 0

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

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

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

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

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

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-5, 2}