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

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


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

Reorder the terms:
(-1 + 3x) * x(x + -5) = 0

Reorder the terms:
(-1 + 3x) * x(-5 + x) = 0

Reorder the terms for easier multiplication:
x(-1 + 3x)(-5 + x) = 0

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

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

Solving
5x + -16x2 + 3x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((1 + -3x)(5 + -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 '(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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