15x^2-9x^3+24x^4=

Solution for 15x^2-9x^3+24x^4= equation:

Simplifying
15x2 + -9x3 + 24x4 = 0

Solving
15x2 + -9x3 + 24x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(5 + -3x + 8x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(5 + -3x + 8x2)' equal to zero and attempt to solve:

Simplifying
5 + -3x + 8x2 = 0

Solving
5 + -3x + 8x2 = 0

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

Divide each side by '8'.
0.625 + -0.375x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -0.375x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -0.375x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -0.375x + x2 = 0 + -0.625
-0.375x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-0.375x + x2 = -0.625

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = -0.625 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = -0.625 + 0.03515625

Combine like terms: -0.625 + 0.03515625 = -0.58984375
0.03515625 + -0.375x + x2 = -0.58984375

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = -0.58984375

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}