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

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


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

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

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

Multiply (-1 + 3x) * (-4 + x)
x(-1(-4 + x) + 3x * (-4 + x)) = 0
x((-4 * -1 + x * -1) + 3x * (-4 + x)) = 0
x((4 + -1x) + 3x * (-4 + x)) = 0
x(4 + -1x + (-4 * 3x + x * 3x)) = 0
x(4 + -1x + (-12x + 3x2)) = 0

Combine like terms: -1x + -12x = -13x
x(4 + -13x + 3x2) = 0
(4 * x + -13x * x + 3x2 * x) = 0
(4x + -13x2 + 3x3) = 0

Solving
4x + -13x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -13x + 3x2) = 0

Factor a trinomial.
x((1 + -3x)(4 + -1x)) = 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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

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

Simplifying
x = 4
Solution
x = {0, 0.3333333333, 4}

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