=2a(4a^2-6a+8)

Solution for =2a(4a^2-6a+8) equation:

Simplifying
0 = 2a(4a2 + -6a + 8)

Reorder the terms:
0 = 2a(8 + -6a + 4a2)
0 = (8 * 2a + -6a * 2a + 4a2 * 2a)
0 = (16a + -12a2 + 8a3)

Solving
0 = 16a + -12a2 + 8a3

Solving for variable 'a'.
Remove the zero:
-16a + 12a2 + -8a3 = 16a + -12a2 + 8a3 + -16a + 12a2 + -8a3

Reorder the terms:
-16a + 12a2 + -8a3 = 16a + -16a + -12a2 + 12a2 + 8a3 + -8a3

Combine like terms: 16a + -16a = 0
-16a + 12a2 + -8a3 = 0 + -12a2 + 12a2 + 8a3 + -8a3
-16a + 12a2 + -8a3 = -12a2 + 12a2 + 8a3 + -8a3

Combine like terms: -12a2 + 12a2 = 0
-16a + 12a2 + -8a3 = 0 + 8a3 + -8a3
-16a + 12a2 + -8a3 = 8a3 + -8a3

Combine like terms: 8a3 + -8a3 = 0
-16a + 12a2 + -8a3 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-4 + 3a + -2a2) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-4 + 3a + -2a2)' equal to zero and attempt to solve:

Simplifying
-4 + 3a + -2a2 = 0

Solving
-4 + 3a + -2a2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2 + -1.5a + a2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.5a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + -1.5a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.5a + a2 = 0 + -2
-1.5a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.5a + a2 = -2

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = -2 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = -2 + 0.5625

Combine like terms: -2 + 0.5625 = -1.4375
0.5625 + -1.5a + a2 = -1.4375

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}