5x(3x+2)=0

Solution for 5x(3x+2)=0 equation:

Simplifying
5x(3x + 2) = 0

Reorder the terms:
5x(2 + 3x) = 0
(2 * 5x + 3x * 5x) = 0
(10x + 15x2) = 0

Solving
10x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(2 + 3x) = 0

Ignore the factor 5.
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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -0.6666666667}