(a-4)(2a+6)=

Solution for (a-4)(2a+6)= equation:

Simplifying
(a + -4)(2a + 6) = 0

Reorder the terms:
(-4 + a)(2a + 6) = 0

Reorder the terms:
(-4 + a)(6 + 2a) = 0

Multiply (-4 + a) * (6 + 2a)
(-4(6 + 2a) + a(6 + 2a)) = 0
((6 * -4 + 2a * -4) + a(6 + 2a)) = 0
((-24 + -8a) + a(6 + 2a)) = 0
(-24 + -8a + (6 * a + 2a * a)) = 0
(-24 + -8a + (6a + 2a2)) = 0

Combine like terms: -8a + 6a = -2a
(-24 + -2a + 2a2) = 0

Solving
-24 + -2a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1a + a2) = 0

Factor a trinomial.
2((-3 + -1a)(4 + -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 '(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
Solution
a = {-3, 4}