(4a+12)(3a+32)=

Solution for (4a+12)(3a+32)= equation:

Simplifying
(4a + 12)(3a + 32) = 0

Reorder the terms:
(12 + 4a)(3a + 32) = 0

Reorder the terms:
(12 + 4a)(32 + 3a) = 0

Multiply (12 + 4a) * (32 + 3a)
(12(32 + 3a) + 4a * (32 + 3a)) = 0
((32 * 12 + 3a * 12) + 4a * (32 + 3a)) = 0
((384 + 36a) + 4a * (32 + 3a)) = 0
(384 + 36a + (32 * 4a + 3a * 4a)) = 0
(384 + 36a + (128a + 12a2)) = 0

Combine like terms: 36a + 128a = 164a
(384 + 164a + 12a2) = 0

Solving
384 + 164a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(96 + 41a + 3a2) = 0

Factor a trinomial.
4((32 + 3a)(3 + a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(32 + 3a)' equal to zero and attempt to solve:

Simplifying
32 + 3a = 0

Solving
32 + 3a = 0

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

Add '-32' to each side of the equation.
32 + -32 + 3a = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 3a = 0 + -32
3a = 0 + -32

Combine like terms: 0 + -32 = -32
3a = -32

Divide each side by '3'.
a = -10.66666667

Simplifying
a = -10.66666667
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {-10.66666667, -3}