4x(x-3)(10-5x)=0

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Solution for 4x(x-3)(10-5x)=0 equation: 


Simplifying
4x(x + -3)(10 + -5x) = 0

Reorder the terms:
4x(-3 + x)(10 + -5x) = 0

Multiply (-3 + x) * (10 + -5x)
4x(-3(10 + -5x) + x(10 + -5x)) = 0
4x((10 * -3 + -5x * -3) + x(10 + -5x)) = 0
4x((-30 + 15x) + x(10 + -5x)) = 0
4x(-30 + 15x + (10 * x + -5x * x)) = 0
4x(-30 + 15x + (10x + -5x2)) = 0

Combine like terms: 15x + 10x = 25x
4x(-30 + 25x + -5x2) = 0
(-30 * 4x + 25x * 4x + -5x2 * 4x) = 0
(-120x + 100x2 + -20x3) = 0

Solving
-120x + 100x2 + -20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20x'.
20x(-6 + 5x + -1x2) = 0

Factor a trinomial.
20x((-3 + x)(2 + -1x)) = 0

Ignore the factor 20.

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 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3

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, 3, 2}

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