12=a(a+1)

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

Simplifying
12 = a(a + 1)

Reorder the terms:
12 = a(1 + a)
12 = (1 * a + a * a)
12 = (1a + a2)

Solving
12 = 1a + a2

Solving for variable 'a'.

Reorder the terms:
12 + -1a + -1a2 = 1a + -1a + a2 + -1a2

Combine like terms: 1a + -1a = 0
12 + -1a + -1a2 = 0 + a2 + -1a2
12 + -1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
12 + -1a + -1a2 = 0

Factor a trinomial.
(3 + -1a)(4 + a) = 0

Subproblem 1
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 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 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Solution
a = {3, -4}