x^2+3(3x-4)-2x(6+2x)=0

Solution for x^2+3(3x-4)-2x(6+2x)=0 equation:

Simplifying
x2 + 3(3x + -4) + -2x(6 + 2x) = 0

Reorder the terms:
x2 + 3(-4 + 3x) + -2x(6 + 2x) = 0
x2 + (-4 * 3 + 3x * 3) + -2x(6 + 2x) = 0
x2 + (-12 + 9x) + -2x(6 + 2x) = 0
x2 + -12 + 9x + (6 * -2x + 2x * -2x) = 0
x2 + -12 + 9x + (-12x + -4x2) = 0

Reorder the terms:
-12 + 9x + -12x + x2 + -4x2 = 0

Combine like terms: 9x + -12x = -3x
-12 + -3x + x2 + -4x2 = 0

Combine like terms: x2 + -4x2 = -3x2
-12 + -3x + -3x2 = 0

Solving
-12 + -3x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(4 + x + x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(4 + x + x2)' equal to zero and attempt to solve:

Simplifying
4 + x + x2 = 0

Solving
4 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x + x2 = 0 + -4
x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
x + x2 = -4

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

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -4 + 0.25

Reorder the terms:
0.25 + x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + x + x2 = -3.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.75

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.