4x^2(3x-2)=0

Solution for 4x^2(3x-2)=0 equation:

Simplifying
4x2(3x + -2) = 0

Reorder the terms:
4x2(-2 + 3x) = 0
(-2 * 4x2 + 3x * 4x2) = 0
(-8x2 + 12x3) = 0

Solving
-8x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-2 + 3x) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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}