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

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


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

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

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

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

Combine like terms: -15x + 1x = -14x
x(-5 + -14x + 3x2) = 0
(-5 * x + -14x * x + 3x2 * x) = 0
(-5x + -14x2 + 3x3) = 0

Solving
-5x + -14x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + -14x + 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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