-12x^5-15x^4+21x^3=0

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Solution for -12x^5-15x^4+21x^3=0 equation: 


Simplifying
-12x5 + -15x4 + 21x3 = 0

Reorder the terms:
21x3 + -15x4 + -12x5 = 0

Solving
21x3 + -15x4 + -12x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(7 + -5x + -4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(7 + -5x + -4x2)' equal to zero and attempt to solve:

Simplifying
7 + -5x + -4x2 = 0

Solving
7 + -5x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.75 + 1.25x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 1.25x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 1.25x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 1.25x + x2 = 0 + 1.75
1.25x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
1.25x + x2 = 1.75

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 1.75 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 1.75 + 0.390625

Combine like terms: 1.75 + 0.390625 = 2.140625
0.390625 + 1.25x + x2 = 2.140625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(x + 0.625) equal to 1.463087489 and -1.463087489.


Subproblem 1
x + 0.625 = 1.463087489

Simplifying
x + 0.625 = 1.463087489

Reorder the terms:
0.625 + x = 1.463087489

Solving
0.625 + x = 1.463087489

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 1.463087489 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 1.463087489 + -0.625
x = 1.463087489 + -0.625

Combine like terms: 1.463087489 + -0.625 = 0.838087489
x = 0.838087489

Simplifying
x = 0.838087489


Subproblem 2
x + 0.625 = -1.463087489

Simplifying
x + 0.625 = -1.463087489

Reorder the terms:
0.625 + x = -1.463087489

Solving
0.625 + x = -1.463087489

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -1.463087489 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -1.463087489 + -0.625
x = -1.463087489 + -0.625

Combine like terms: -1.463087489 + -0.625 = -2.088087489
x = -2.088087489

Simplifying
x = -2.088087489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.838087489, -2.088087489}
Solution
x = {0.838087489, -2.088087489}

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