2x(1-3x)(5-x)=0

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Solution for 2x(1-3x)(5-x)=0 equation: 


Simplifying
2x(1 + -3x)(5 + -1x) = 0

Multiply (1 + -3x) * (5 + -1x)
2x(1(5 + -1x) + -3x * (5 + -1x)) = 0
2x((5 * 1 + -1x * 1) + -3x * (5 + -1x)) = 0
2x((5 + -1x) + -3x * (5 + -1x)) = 0
2x(5 + -1x + (5 * -3x + -1x * -3x)) = 0
2x(5 + -1x + (-15x + 3x2)) = 0

Combine like terms: -1x + -15x = -16x
2x(5 + -16x + 3x2) = 0
(5 * 2x + -16x * 2x + 3x2 * 2x) = 0
(10x + -32x2 + 6x3) = 0

Solving
10x + -32x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + -16x + 3x2) = 0

Factor a trinomial.
2x((1 + -3x)(5 + -1x)) = 0

Ignore the factor 2.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 0.3333333333, 5}

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