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

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

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

Reorder the terms:
7a + -4a + 7ab + -1ab = 0

Combine like terms: 7a + -4a = 3a
3a + 7ab + -1ab = 0

Combine like terms: 7ab + -1ab = 6ab
3a + 6ab = 0

Solving
3a + 6ab = 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(1 + 2b) = 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 '(1 + 2b)' equal to zero and attempt to solve:

Simplifying
1 + 2b = 0

Solving
1 + 2b = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2b = 0 + -1
2b = 0 + -1

Combine like terms: 0 + -1 = -1
2b = -1

Add '-2b' to each side of the equation.
2b + -2b = -1 + -2b

Combine like terms: 2b + -2b = 0
0 = -1 + -2b

Simplifying
0 = -1 + -2b

The solution to this equation could not be determined.

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