4(2a^2-6)-3a(4a-8)=

Solution for 4(2a^2-6)-3a(4a-8)= equation:

Simplifying
4(2a2 + -6) + -3a(4a + -8) = 0

Reorder the terms:
4(-6 + 2a2) + -3a(4a + -8) = 0
(-6 * 4 + 2a2 * 4) + -3a(4a + -8) = 0
(-24 + 8a2) + -3a(4a + -8) = 0

Reorder the terms:
-24 + 8a2 + -3a(-8 + 4a) = 0
-24 + 8a2 + (-8 * -3a + 4a * -3a) = 0
-24 + 8a2 + (24a + -12a2) = 0

Reorder the terms:
-24 + 24a + 8a2 + -12a2 = 0

Combine like terms: 8a2 + -12a2 = -4a2
-24 + 24a + -4a2 = 0

Solving
-24 + 24a + -4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 6a + -1a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + 6a + -1a2)' equal to zero and attempt to solve:

Simplifying
-6 + 6a + -1a2 = 0

Solving
-6 + 6a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -6a + a2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -6a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + -6a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -6a + a2 = 0 + -6
-6a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
-6a + a2 = -6

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -6 + 9

Reorder the terms:
9 + -6a + a2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + -6a + a2 = 3

Factor a perfect square on the left side:
(a + -3)(a + -3) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
a + -3 = 1.732050808

Simplifying
a + -3 = 1.732050808

Reorder the terms:
-3 + a = 1.732050808

Solving
-3 + a = 1.732050808

Solving for variable 'a'.

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

Add '3' to each side of the equation.
-3 + 3 + a = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + a = 1.732050808 + 3
a = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
a = 4.732050808

Simplifying
a = 4.732050808

Subproblem 2
a + -3 = -1.732050808

Simplifying
a + -3 = -1.732050808

Reorder the terms:
-3 + a = -1.732050808

Solving
-3 + a = -1.732050808

Solving for variable 'a'.

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

Add '3' to each side of the equation.
-3 + 3 + a = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + a = -1.732050808 + 3
a = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
a = 1.267949192

Simplifying
a = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.732050808, 1.267949192}
Solution
a = {4.732050808, 1.267949192}