4x((-3+x)(3+-1x))=0

Solution for 4x((-3+x)(3+-1x))=0 equation:

Simplifying
4x((-3 + x)(3 + -1x)) = 0

Multiply (-3 + x) * (3 + -1x)
4x((-3(3 + -1x) + x(3 + -1x))) = 0
4x(((3 * -3 + -1x * -3) + x(3 + -1x))) = 0
4x(((-9 + 3x) + x(3 + -1x))) = 0
4x((-9 + 3x + (3 * x + -1x * x))) = 0
4x((-9 + 3x + (3x + -1x2))) = 0

Combine like terms: 3x + 3x = 6x
4x((-9 + 6x + -1x2)) = 0
(-9 * 4x + 6x * 4x + -1x2 * 4x) = 0
(-36x + 24x2 + -4x3) = 0

Solving
-36x + 24x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-9 + 6x + -1x2) = 0

Factor a trinomial.
4x((-3 + x)(3 + -1x)) = 0

Ignore the factor 4.
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 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3, 3}