(a-4)(4a+4)=

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

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

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

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

Multiply (-4 + a) * (4 + 4a)
(-4(4 + 4a) + a(4 + 4a)) = 0
((4 * -4 + 4a * -4) + a(4 + 4a)) = 0
((-16 + -16a) + a(4 + 4a)) = 0
(-16 + -16a + (4 * a + 4a * a)) = 0
(-16 + -16a + (4a + 4a2)) = 0

Combine like terms: -16a + 4a = -12a
(-16 + -12a + 4a2) = 0

Solving
-16 + -12a + 4a2 = 0

Solving for variable 'a'.

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

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
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 = {-1, 4}