8(3a-5)4(2a+3)=12

Solution for 8(3a-5)4(2a+3)=12 equation:

Simplifying
8(3a + -5) * 4(2a + 3) = 12

Reorder the terms:
8(-5 + 3a) * 4(2a + 3) = 12

Reorder the terms:
8(-5 + 3a) * 4(3 + 2a) = 12

Reorder the terms for easier multiplication:
8 * 4(-5 + 3a)(3 + 2a) = 12

Multiply 8 * 4
32(-5 + 3a)(3 + 2a) = 12

Multiply (-5 + 3a) * (3 + 2a)
32(-5(3 + 2a) + 3a * (3 + 2a)) = 12
32((3 * -5 + 2a * -5) + 3a * (3 + 2a)) = 12
32((-15 + -10a) + 3a * (3 + 2a)) = 12
32(-15 + -10a + (3 * 3a + 2a * 3a)) = 12
32(-15 + -10a + (9a + 6a2)) = 12

Combine like terms: -10a + 9a = -1a
32(-15 + -1a + 6a2) = 12
(-15 * 32 + -1a * 32 + 6a2 * 32) = 12
(-480 + -32a + 192a2) = 12

Solving
-480 + -32a + 192a2 = 12

Solving for variable 'a'.

Reorder the terms:
-480 + -12 + -32a + 192a2 = 12 + -12

Combine like terms: -480 + -12 = -492
-492 + -32a + 192a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-492 + -32a + 192a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-123 + -8a + 48a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-123 + -8a + 48a2)' equal to zero and attempt to solve:

Simplifying
-123 + -8a + 48a2 = 0

Solving
-123 + -8a + 48a2 = 0

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

Divide each side by '48'.
-2.5625 + -0.1666666667a + a2 = 0

Move the constant term to the right:

Add '2.5625' to each side of the equation.
-2.5625 + -0.1666666667a + 2.5625 + a2 = 0 + 2.5625

Reorder the terms:
-2.5625 + 2.5625 + -0.1666666667a + a2 = 0 + 2.5625

Combine like terms: -2.5625 + 2.5625 = 0.0000
0.0000 + -0.1666666667a + a2 = 0 + 2.5625
-0.1666666667a + a2 = 0 + 2.5625

Combine like terms: 0 + 2.5625 = 2.5625
-0.1666666667a + a2 = 2.5625

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 = 2.5625 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667a + a2 = 2.5625 + 0.006944444447

Combine like terms: 2.5625 + 0.006944444447 = 2.569444444447
0.006944444447 + -0.1666666667a + a2 = 2.569444444447

Factor a perfect square on the left side:
(a + -0.08333333335)(a + -0.08333333335) = 2.569444444447

Calculate the square root of the right side: 1.602948672

Break this problem into two subproblems by setting 
(a + -0.08333333335) equal to 1.602948672 and -1.602948672.

Subproblem 1
a + -0.08333333335 = 1.602948672

Simplifying
a + -0.08333333335 = 1.602948672

Reorder the terms:
-0.08333333335 + a = 1.602948672

Solving
-0.08333333335 + a = 1.602948672

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 = 1.602948672 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + a = 1.602948672 + 0.08333333335
a = 1.602948672 + 0.08333333335

Combine like terms: 1.602948672 + 0.08333333335 = 1.68628200535
a = 1.68628200535

Simplifying
a = 1.68628200535

Subproblem 2
a + -0.08333333335 = -1.602948672

Simplifying
a + -0.08333333335 = -1.602948672

Reorder the terms:
-0.08333333335 + a = -1.602948672

Solving
-0.08333333335 + a = -1.602948672

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 = -1.602948672 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + a = -1.602948672 + 0.08333333335
a = -1.602948672 + 0.08333333335

Combine like terms: -1.602948672 + 0.08333333335 = -1.51961533865
a = -1.51961533865

Simplifying
a = -1.51961533865

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.68628200535, -1.51961533865}
Solution
a = {1.68628200535, -1.51961533865}