3(12)=a(a+5)

Solution for 3(12)=a(a+5) equation:

Simplifying
3(12) = a(a + 5)

Multiply 3 * 12
36 = a(a + 5)

Reorder the terms:
36 = a(5 + a)
36 = (5 * a + a * a)
36 = (5a + a2)

Solving
36 = 5a + a2

Solving for variable 'a'.

Reorder the terms:
36 + -5a + -1a2 = 5a + -5a + a2 + -1a2

Combine like terms: 5a + -5a = 0
36 + -5a + -1a2 = 0 + a2 + -1a2
36 + -5a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
36 + -5a + -1a2 = 0

Factor a trinomial.
(4 + -1a)(9 + a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + a)' equal to zero and attempt to solve:

Simplifying
9 + a = 0

Solving
9 + a = 0

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

Add '-9' to each side of the equation.
9 + -9 + a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + a = 0 + -9
a = 0 + -9

Combine like terms: 0 + -9 = -9
a = -9

Simplifying
a = -9
Solution
a = {4, -9}