3x(2x-5)(x-4)=0

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Solution for 3x(2x-5)(x-4)=0 equation: 


Simplifying
3x(2x + -5)(x + -4) = 0

Reorder the terms:
3x(-5 + 2x)(x + -4) = 0

Reorder the terms:
3x(-5 + 2x)(-4 + x) = 0

Multiply (-5 + 2x) * (-4 + x)
3x(-5(-4 + x) + 2x * (-4 + x)) = 0
3x((-4 * -5 + x * -5) + 2x * (-4 + x)) = 0
3x((20 + -5x) + 2x * (-4 + x)) = 0
3x(20 + -5x + (-4 * 2x + x * 2x)) = 0
3x(20 + -5x + (-8x + 2x2)) = 0

Combine like terms: -5x + -8x = -13x
3x(20 + -13x + 2x2) = 0
(20 * 3x + -13x * 3x + 2x2 * 3x) = 0
(60x + -39x2 + 6x3) = 0

Solving
60x + -39x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(20 + -13x + 2x2) = 0

Factor a trinomial.
3x((5 + -2x)(4 + -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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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, 2.5, 4}

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