4a(7b+12a)=0

Solution for 4a(7b+12a)=0 equation:

Simplifying
4a(7b + 12a) = 0

Reorder the terms:
4a(12a + 7b) = 0
(12a * 4a + 7b * 4a) = 0

Reorder the terms:
(28ab + 48a2) = 0
(28ab + 48a2) = 0

Solving
28ab + 48a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(7b + 12a) = 0

Ignore the factor 4.
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 '(7b + 12a)' equal to zero and attempt to solve:

Simplifying
7b + 12a = 0

Reorder the terms:
12a + 7b = 0

Solving
12a + 7b = 0

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

Add '-7b' to each side of the equation.
12a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
12a + 0 = 0 + -7b
12a = 0 + -7b
Remove the zero:
12a = -7b

Divide each side by '12'.
a = -0.5833333333b

Simplifying
a = -0.5833333333b
Solution
a = {0, -0.5833333333b}