(6a+8)(a+4)=

Solution for (6a+8)(a+4)= equation:

Simplifying
(6a + 8)(a + 4) = 0

Reorder the terms:
(8 + 6a)(a + 4) = 0

Reorder the terms:
(8 + 6a)(4 + a) = 0

Multiply (8 + 6a) * (4 + a)
(8(4 + a) + 6a * (4 + a)) = 0
((4 * 8 + a * 8) + 6a * (4 + a)) = 0
((32 + 8a) + 6a * (4 + a)) = 0
(32 + 8a + (4 * 6a + a * 6a)) = 0
(32 + 8a + (24a + 6a2)) = 0

Combine like terms: 8a + 24a = 32a
(32 + 32a + 6a2) = 0

Solving
32 + 32a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 16a + 3a2) = 0

Factor a trinomial.
2((4 + a)(4 + 3a)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + 3a)' equal to zero and attempt to solve:

Simplifying
4 + 3a = 0

Solving
4 + 3a = 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 + 3a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3a = 0 + -4
3a = 0 + -4

Combine like terms: 0 + -4 = -4
3a = -4

Divide each side by '3'.
a = -1.333333333

Simplifying
a = -1.333333333
Solution
a = {-4, -1.333333333}