-6(3-3a)8(6a+5)=32

Solution for -6(3-3a)8(6a+5)=32 equation:

Simplifying
-6(3 + -3a) * 8(6a + 5) = 32

Reorder the terms:
-6(3 + -3a) * 8(5 + 6a) = 32

Reorder the terms for easier multiplication:
-6 * 8(3 + -3a)(5 + 6a) = 32

Multiply -6 * 8
-48(3 + -3a)(5 + 6a) = 32

Multiply (3 + -3a) * (5 + 6a)
-48(3(5 + 6a) + -3a * (5 + 6a)) = 32
-48((5 * 3 + 6a * 3) + -3a * (5 + 6a)) = 32
-48((15 + 18a) + -3a * (5 + 6a)) = 32
-48(15 + 18a + (5 * -3a + 6a * -3a)) = 32
-48(15 + 18a + (-15a + -18a2)) = 32

Combine like terms: 18a + -15a = 3a
-48(15 + 3a + -18a2) = 32
(15 * -48 + 3a * -48 + -18a2 * -48) = 32
(-720 + -144a + 864a2) = 32

Solving
-720 + -144a + 864a2 = 32

Solving for variable 'a'.

Reorder the terms:
-720 + -32 + -144a + 864a2 = 32 + -32

Combine like terms: -720 + -32 = -752
-752 + -144a + 864a2 = 32 + -32

Combine like terms: 32 + -32 = 0
-752 + -144a + 864a2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-47 + -9a + 54a2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-47 + -9a + 54a2)' equal to zero and attempt to solve:

Simplifying
-47 + -9a + 54a2 = 0

Solving
-47 + -9a + 54a2 = 0

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

Divide each side by '54'.
-0.8703703704 + -0.1666666667a + a2 = 0

Move the constant term to the right:

Add '0.8703703704' to each side of the equation.
-0.8703703704 + -0.1666666667a + 0.8703703704 + a2 = 0 + 0.8703703704

Reorder the terms:
-0.8703703704 + 0.8703703704 + -0.1666666667a + a2 = 0 + 0.8703703704

Combine like terms: -0.8703703704 + 0.8703703704 = 0.0000000000
0.0000000000 + -0.1666666667a + a2 = 0 + 0.8703703704
-0.1666666667a + a2 = 0 + 0.8703703704

Combine like terms: 0 + 0.8703703704 = 0.8703703704
-0.1666666667a + a2 = 0.8703703704

The a term is -0.1666666667a.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667a + 0.006944444447 + a2 = 0.8703703704 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667a + a2 = 0.8703703704 + 0.006944444447

Combine like terms: 0.8703703704 + 0.006944444447 = 0.877314814847
0.006944444447 + -0.1666666667a + a2 = 0.877314814847

Factor a perfect square on the left side:
(a + -0.08333333335)(a + -0.08333333335) = 0.877314814847

Calculate the square root of the right side: 0.93665085

Break this problem into two subproblems by setting 
(a + -0.08333333335) equal to 0.93665085 and -0.93665085.

Subproblem 1
a + -0.08333333335 = 0.93665085

Simplifying
a + -0.08333333335 = 0.93665085

Reorder the terms:
-0.08333333335 + a = 0.93665085

Solving
-0.08333333335 + a = 0.93665085

Solving for variable 'a'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + a = 0.93665085 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + a = 0.93665085 + 0.08333333335
a = 0.93665085 + 0.08333333335

Combine like terms: 0.93665085 + 0.08333333335 = 1.01998418335
a = 1.01998418335

Simplifying
a = 1.01998418335

Subproblem 2
a + -0.08333333335 = -0.93665085

Simplifying
a + -0.08333333335 = -0.93665085

Reorder the terms:
-0.08333333335 + a = -0.93665085

Solving
-0.08333333335 + a = -0.93665085

Solving for variable 'a'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + a = -0.93665085 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + a = -0.93665085 + 0.08333333335
a = -0.93665085 + 0.08333333335

Combine like terms: -0.93665085 + 0.08333333335 = -0.85331751665
a = -0.85331751665

Simplifying
a = -0.85331751665

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.01998418335, -0.85331751665}
Solution
a = {1.01998418335, -0.85331751665}