9x^2(x+1)+6x(5+x)=

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Solution for 9x^2(x+1)+6x(5+x)= equation: 


Simplifying
9x2(x + 1) + 6x(5 + x) = 0

Reorder the terms:
9x2(1 + x) + 6x(5 + x) = 0
(1 * 9x2 + x * 9x2) + 6x(5 + x) = 0
(9x2 + 9x3) + 6x(5 + x) = 0
9x2 + 9x3 + (5 * 6x + x * 6x) = 0
9x2 + 9x3 + (30x + 6x2) = 0

Reorder the terms:
30x + 9x2 + 6x2 + 9x3 = 0

Combine like terms: 9x2 + 6x2 = 15x2
30x + 15x2 + 9x3 = 0

Solving
30x + 15x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(10 + 5x + 3x2) = 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 '(10 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
10 + 5x + 3x2 = 0

Solving
10 + 5x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 1.666666667x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 1.666666667x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + -3.333333333
1.666666667x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
1.666666667x + x2 = -3.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -3.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -3.333333333 + 0.6944444447

Combine like terms: -3.333333333 + 0.6944444447 = -2.6388888883
0.6944444447 + 1.666666667x + x2 = -2.6388888883

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -2.6388888883

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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