3x(4x-1)(x-2)=0

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Solution for 3x(4x-1)(x-2)=0 equation: 


Simplifying
3x(4x + -1)(x + -2) = 0

Reorder the terms:
3x(-1 + 4x)(x + -2) = 0

Reorder the terms:
3x(-1 + 4x)(-2 + x) = 0

Multiply (-1 + 4x) * (-2 + x)
3x(-1(-2 + x) + 4x * (-2 + x)) = 0
3x((-2 * -1 + x * -1) + 4x * (-2 + x)) = 0
3x((2 + -1x) + 4x * (-2 + x)) = 0
3x(2 + -1x + (-2 * 4x + x * 4x)) = 0
3x(2 + -1x + (-8x + 4x2)) = 0

Combine like terms: -1x + -8x = -9x
3x(2 + -9x + 4x2) = 0
(2 * 3x + -9x * 3x + 4x2 * 3x) = 0
(6x + -27x2 + 12x3) = 0

Solving
6x + -27x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(2 + -9x + 4x2) = 0

Factor a trinomial.
3x((1 + -4x)(2 + -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 '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 0.25, 2}

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