7a(1+b)-4a(4+b)=0

Solution for 7a(1+b)-4a(4+b)=0 equation:

Simplifying
7a(1 + b) + -4a(4 + b) = 0
(1 * 7a + b * 7a) + -4a(4 + b) = 0
(7a + 7ab) + -4a(4 + b) = 0
7a + 7ab + (4 * -4a + b * -4a) = 0
7a + 7ab + (-16a + -4ab) = 0

Reorder the terms:
7a + -16a + 7ab + -4ab = 0

Combine like terms: 7a + -16a = -9a
-9a + 7ab + -4ab = 0

Combine like terms: 7ab + -4ab = 3ab
-9a + 3ab = 0

Solving
-9a + 3ab = 0

Solving for variable 'a'.

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

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

Ignore the factor 3.
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 '(-3 + b)' equal to zero and attempt to solve:

Simplifying
-3 + b = 0

Solving
-3 + b = 0

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

Add '3' to each side of the equation.
-3 + 3 + b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + b = 0 + 3
b = 0 + 3

Combine like terms: 0 + 3 = 3
b = 3

Add '-1b' to each side of the equation.
b + -1b = 3 + -1b

Combine like terms: b + -1b = 0
0 = 3 + -1b

Simplifying
0 = 3 + -1b

The solution to this equation could not be determined.

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