3x^3+15x^2+75x=0

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Solution for 3x^3+15x^2+75x=0 equation: 


Simplifying
3x3 + 15x2 + 75x = 0

Reorder the terms:
75x + 15x2 + 3x3 = 0

Solving
75x + 15x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(25 + 5x + x2) = 0

Ignore the factor 3.

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 '(25 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
25 + 5x + x2 = 0

Solving
25 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 5x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 5x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 5x + x2 = 0 + -25
5x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
5x + x2 = -25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -25 + 6.25

Combine like terms: -25 + 6.25 = -18.75
6.25 + 5x + x2 = -18.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -18.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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