(a+3)(a-12)=0

Solution for (a+3)(a-12)=0 equation:

Simplifying
(a + 3)(a + -12) = 0

Reorder the terms:
(3 + a)(a + -12) = 0

Reorder the terms:
(3 + a)(-12 + a) = 0

Multiply (3 + a) * (-12 + a)
(3(-12 + a) + a(-12 + a)) = 0
((-12 * 3 + a * 3) + a(-12 + a)) = 0
((-36 + 3a) + a(-12 + a)) = 0
(-36 + 3a + (-12 * a + a * a)) = 0
(-36 + 3a + (-12a + a2)) = 0

Combine like terms: 3a + -12a = -9a
(-36 + -9a + a2) = 0

Solving
-36 + -9a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(12 + -1a) = 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 '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

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

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

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-3, 12}