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

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


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

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

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

Multiply (-3 + 5x) * (-4 + x)
x(-3(-4 + x) + 5x * (-4 + x)) = 0
x((-4 * -3 + x * -3) + 5x * (-4 + x)) = 0
x((12 + -3x) + 5x * (-4 + x)) = 0
x(12 + -3x + (-4 * 5x + x * 5x)) = 0
x(12 + -3x + (-20x + 5x2)) = 0

Combine like terms: -3x + -20x = -23x
x(12 + -23x + 5x2) = 0
(12 * x + -23x * x + 5x2 * x) = 0
(12x + -23x2 + 5x3) = 0

Solving
12x + -23x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + -23x + 5x2) = 0

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

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6

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, 0.6, 4}

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