4a(2b-3+ab)+3(4ab-b+4a)=

Solution for 4a(2b-3+ab)+3(4ab-b+4a)= equation:

Simplifying
4a(2b + -3 + ab) + 3(4ab + -1b + 4a) = 0

Reorder the terms:
4a(-3 + ab + 2b) + 3(4ab + -1b + 4a) = 0
(-3 * 4a + ab * 4a + 2b * 4a) + 3(4ab + -1b + 4a) = 0

Reorder the terms:
(-12a + 8ab + 4a2b) + 3(4ab + -1b + 4a) = 0
(-12a + 8ab + 4a2b) + 3(4ab + -1b + 4a) = 0

Reorder the terms:
-12a + 8ab + 4a2b + 3(4a + 4ab + -1b) = 0
-12a + 8ab + 4a2b + (4a * 3 + 4ab * 3 + -1b * 3) = 0
-12a + 8ab + 4a2b + (12a + 12ab + -3b) = 0

Reorder the terms:
-12a + 12a + 8ab + 12ab + 4a2b + -3b = 0

Combine like terms: -12a + 12a = 0
0 + 8ab + 12ab + 4a2b + -3b = 0
8ab + 12ab + 4a2b + -3b = 0

Combine like terms: 8ab + 12ab = 20ab
20ab + 4a2b + -3b = 0

Solving
20ab + 4a2b + -3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(20a + 4a2 + -3) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(20a + 4a2 + -3)' equal to zero and attempt to solve:

Simplifying
20a + 4a2 + -3 = 0

Reorder the terms:
-3 + 20a + 4a2 = 0

Solving
-3 + 20a + 4a2 = 0

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

Divide each side by '4'.
-0.75 + 5a + a2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 5a + 0.75 + a2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 5a + a2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 5a + a2 = 0 + 0.75
5a + a2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
5a + a2 = 0.75

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 0.75 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 0.75 + 6.25

Combine like terms: 0.75 + 6.25 = 7
6.25 + 5a + a2 = 7

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(a + 2.5) equal to 2.645751311 and -2.645751311.

Subproblem 1
a + 2.5 = 2.645751311

Simplifying
a + 2.5 = 2.645751311

Reorder the terms:
2.5 + a = 2.645751311

Solving
2.5 + a = 2.645751311

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = 2.645751311 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = 2.645751311 + -2.5
a = 2.645751311 + -2.5

Combine like terms: 2.645751311 + -2.5 = 0.145751311
a = 0.145751311

Simplifying
a = 0.145751311

Subproblem 2
a + 2.5 = -2.645751311

Simplifying
a + 2.5 = -2.645751311

Reorder the terms:
2.5 + a = -2.645751311

Solving
2.5 + a = -2.645751311

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = -2.645751311 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = -2.645751311 + -2.5
a = -2.645751311 + -2.5

Combine like terms: -2.645751311 + -2.5 = -5.145751311
a = -5.145751311

Simplifying
a = -5.145751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.145751311, -5.145751311}
Solution
a = {0.145751311, -5.145751311}