2a*(a+1)=12

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

Simplifying
2a(a + 1) = 12

Reorder the terms:
2a(1 + a) = 12
(1 * 2a + a * 2a) = 12
(2a + 2a2) = 12

Solving
2a + 2a2 = 12

Solving for variable 'a'.

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

Combine like terms: 12 + -12 = 0
-12 + 2a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + a + a2) = 0

Factor a trinomial.
2((-3 + -1a)(2 + -1a)) = 0

Ignore the factor 2.
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 '(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 = {-3, 2}