6x(x^2+3)-3x(x+5)=0

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Solution for 6x(x^2+3)-3x(x+5)=0 equation: 


Simplifying
6x(x2 + 3) + -3x(x + 5) = 0

Reorder the terms:
6x(3 + x2) + -3x(x + 5) = 0
(3 * 6x + x2 * 6x) + -3x(x + 5) = 0
(18x + 6x3) + -3x(x + 5) = 0

Reorder the terms:
18x + 6x3 + -3x(5 + x) = 0
18x + 6x3 + (5 * -3x + x * -3x) = 0
18x + 6x3 + (-15x + -3x2) = 0

Reorder the terms:
18x + -15x + -3x2 + 6x3 = 0

Combine like terms: 18x + -15x = 3x
3x + -3x2 + 6x3 = 0

Solving
3x + -3x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + -1x + 2x2) = 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 '(1 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + 2x2 = 0

Solving
1 + -1x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.5x + x2 = 0 + -0.5
-0.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.5x + x2 = -0.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.5 + 0.0625

Combine like terms: -0.5 + 0.0625 = -0.4375
0.0625 + -0.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.4375

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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