2(x-3+2x)-x(2+6+3x)=

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

Simplifying
2(x + -3 + 2x) + -1x(2 + 6 + 3x) = 0

Reorder the terms:
2(-3 + x + 2x) + -1x(2 + 6 + 3x) = 0

Combine like terms: x + 2x = 3x
2(-3 + 3x) + -1x(2 + 6 + 3x) = 0
(-3 * 2 + 3x * 2) + -1x(2 + 6 + 3x) = 0
(-6 + 6x) + -1x(2 + 6 + 3x) = 0

Combine like terms: 2 + 6 = 8
-6 + 6x + -1x(8 + 3x) = 0
-6 + 6x + (8 * -1x + 3x * -1x) = 0
-6 + 6x + (-8x + -3x2) = 0

Combine like terms: 6x + -8x = -2x
-6 + -2x + -3x2 = 0

Solving
-6 + -2x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 2x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
6 + 2x + 3x2 = 0

Solving
6 + 2x + 3x2 = 0

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

Divide each side by '3'.
2 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.6666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 0.6666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.6666666667x + x2 = 0 + -2
0.6666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.6666666667x + x2 = -2

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + 0.6666666667x + x2 = -1.8888888888

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = -1.8888888888

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.