a(4a+3)=0

Solution for a(4a+3)=0 equation:

Simplifying
a(4a + 3) = 0

Reorder the terms:
a(3 + 4a) = 0
(3 * a + 4a * a) = 0
(3a + 4a2) = 0

Solving
3a + 4a2 = 0

Solving for variable 'a'.

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

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 + 4a)' equal to zero and attempt to solve:

Simplifying
3 + 4a = 0

Solving
3 + 4a = 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 + 4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4a = 0 + -3
4a = 0 + -3

Combine like terms: 0 + -3 = -3
4a = -3

Divide each side by '4'.
a = -0.75

Simplifying
a = -0.75
Solution
a = {0, -0.75}