3x^2-9(x^2+3x)=32

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Solution for 3x^2-9(x^2+3x)=32 equation: 


Simplifying
3x2 + -9(x2 + 3x) = 32

Reorder the terms:
3x2 + -9(3x + x2) = 32
3x2 + (3x * -9 + x2 * -9) = 32
3x2 + (-27x + -9x2) = 32

Reorder the terms:
-27x + 3x2 + -9x2 = 32

Combine like terms: 3x2 + -9x2 = -6x2
-27x + -6x2 = 32

Solving
-27x + -6x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + -27x + -6x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -27x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 27x + 6x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(32 + 27x + 6x2)' equal to zero and attempt to solve:

Simplifying
32 + 27x + 6x2 = 0

Solving
32 + 27x + 6x2 = 0

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

Divide each side by '6'.
5.333333333 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + 4.5x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + 4.5x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + 4.5x + x2 = 0 + -5.333333333
4.5x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
4.5x + x2 = -5.333333333

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -5.333333333 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -5.333333333 + 5.0625

Combine like terms: -5.333333333 + 5.0625 = -0.270833333
5.0625 + 4.5x + x2 = -0.270833333

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = -0.270833333

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.

The solution to this equation could not be determined.

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