(a+6)(a*2-8a+8)=

Solution for (a+6)(a*2-8a+8)= equation:

Simplifying
(a + 6)(a * 2 + -8a + 8) = 0

Reorder the terms:
(6 + a)(a * 2 + -8a + 8) = 0

Reorder the terms for easier multiplication:
(6 + a)(2a + -8a + 8) = 0

Reorder the terms:
(6 + a)(8 + 2a + -8a) = 0

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

Multiply (6 + a) * (8 + -6a)
(6(8 + -6a) + a(8 + -6a)) = 0
((8 * 6 + -6a * 6) + a(8 + -6a)) = 0
((48 + -36a) + a(8 + -6a)) = 0
(48 + -36a + (8 * a + -6a * a)) = 0
(48 + -36a + (8a + -6a2)) = 0

Combine like terms: -36a + 8a = -28a
(48 + -28a + -6a2) = 0

Solving
48 + -28a + -6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -14a + -3a2) = 0

Factor a trinomial.
2((4 + -3a)(6 + a)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {1.333333333, -6}