4x^2y+3x=0

Solution for 4x^2y+3x=0 equation:

Simplifying
4x2y + 3x = 0

Reorder the terms:
3x + 4x2y = 0

Solving
3x + 4x2y = 0

Solving for variable 'x'.

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

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + 4xy)' equal to zero and attempt to solve:

Simplifying
3 + 4xy = 0

Solving
3 + 4xy = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4xy = 0 + -3

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

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

Divide each side by '4y'.
x = -0.75y-1

Simplifying
x = -0.75y-1
Solution
x = {0, -0.75y-1}