10x(6x^2+7x+9)=0

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Solution for 10x(6x^2+7x+9)=0 equation: 


Simplifying
10x(6x2 + 7x + 9) = 0

Reorder the terms:
10x(9 + 7x + 6x2) = 0
(9 * 10x + 7x * 10x + 6x2 * 10x) = 0
(90x + 70x2 + 60x3) = 0

Solving
90x + 70x2 + 60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x'.
10x(9 + 7x + 6x2) = 0

Ignore the factor 10.

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 '(9 + 7x + 6x2)' equal to zero and attempt to solve:

Simplifying
9 + 7x + 6x2 = 0

Solving
9 + 7x + 6x2 = 0

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

Divide each side by '6'.
1.5 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 1.166666667x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 1.166666667x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 1.166666667x + x2 = 0 + -1.5
1.166666667x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
1.166666667x + x2 = -1.5

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = -1.5 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = -1.5 + 0.3402777780

Combine like terms: -1.5 + 0.3402777780 = -1.159722222
0.3402777780 + 1.166666667x + x2 = -1.159722222

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = -1.159722222

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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