12x^3-x^2=15x

Solution for 12x^3-x^2=15x equation:

Simplifying
12x3 + -1x2 = 15x

Reorder the terms:
-1x2 + 12x3 = 15x

Solving
-1x2 + 12x3 = 15x

Solving for variable 'x'.

Reorder the terms:
-15x + -1x2 + 12x3 = 15x + -15x

Combine like terms: 15x + -15x = 0
-15x + -1x2 + 12x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + -1x + 12x2) = 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 '(-15 + -1x + 12x2)' equal to zero and attempt to solve:

Simplifying
-15 + -1x + 12x2 = 0

Solving
-15 + -1x + 12x2 = 0

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

Divide each side by '12'.
-1.25 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.08333333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.08333333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.08333333333x + x2 = 0 + 1.25
-0.08333333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.08333333333x + x2 = 1.25

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 1.25 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 1.25 + 0.001736111111

Combine like terms: 1.25 + 0.001736111111 = 1.251736111111
0.001736111111 + -0.08333333333x + x2 = 1.251736111111

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 1.251736111111

Calculate the square root of the right side: 1.118810132

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 1.118810132 and -1.118810132.

Subproblem 1
x + -0.04166666667 = 1.118810132

Simplifying
x + -0.04166666667 = 1.118810132

Reorder the terms:
-0.04166666667 + x = 1.118810132

Solving
-0.04166666667 + x = 1.118810132

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = 1.118810132 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = 1.118810132 + 0.04166666667
x = 1.118810132 + 0.04166666667

Combine like terms: 1.118810132 + 0.04166666667 = 1.16047679867
x = 1.16047679867

Simplifying
x = 1.16047679867

Subproblem 2
x + -0.04166666667 = -1.118810132

Simplifying
x + -0.04166666667 = -1.118810132

Reorder the terms:
-0.04166666667 + x = -1.118810132

Solving
-0.04166666667 + x = -1.118810132

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = -1.118810132 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = -1.118810132 + 0.04166666667
x = -1.118810132 + 0.04166666667

Combine like terms: -1.118810132 + 0.04166666667 = -1.07714346533
x = -1.07714346533

Simplifying
x = -1.07714346533

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.16047679867, -1.07714346533}
Solution
x = {0, 1.16047679867, -1.07714346533}