5x^3+4x^2+60x=0

Solution for 5x^3+4x^2+60x=0 equation:

Simplifying
5x3 + 4x2 + 60x = 0

Reorder the terms:
60x + 4x2 + 5x3 = 0

Solving
60x + 4x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(60 + 4x + 5x2) = 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 '(60 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
60 + 4x + 5x2 = 0

Solving
60 + 4x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
12 + 0.8x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 0.8x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 0.8x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 0.8x + x2 = 0 + -12
0.8x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
0.8x + x2 = -12

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = -12 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = -12 + 0.16

Combine like terms: -12 + 0.16 = -11.84
0.16 + 0.8x + x2 = -11.84

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = -11.84

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}