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

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


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

Reorder the terms:
0 = 3x(-4 + x)(x + -1)

Reorder the terms:
0 = 3x(-4 + x)(-1 + x)

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

Combine like terms: -4x + -1x = -5x
0 = 3x(4 + -5x + x2)
0 = (4 * 3x + -5x * 3x + x2 * 3x)
0 = (12x + -15x2 + 3x3)

Solving
0 = 12x + -15x2 + 3x3

Solving for variable 'x'.
Remove the zero:
-12x + 15x2 + -3x3 = 12x + -15x2 + 3x3 + -12x + 15x2 + -3x3

Reorder the terms:
-12x + 15x2 + -3x3 = 12x + -12x + -15x2 + 15x2 + 3x3 + -3x3

Combine like terms: 12x + -12x = 0
-12x + 15x2 + -3x3 = 0 + -15x2 + 15x2 + 3x3 + -3x3
-12x + 15x2 + -3x3 = -15x2 + 15x2 + 3x3 + -3x3

Combine like terms: -15x2 + 15x2 = 0
-12x + 15x2 + -3x3 = 0 + 3x3 + -3x3
-12x + 15x2 + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
-12x + 15x2 + -3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + 5x + -1x2) = 0

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

Ignore the factor 3.

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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {0, 4, 1}

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