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

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

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

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

Reorder the terms:
6x + -2x2 = 6 + 4x

Solving
6x + -2x2 = 6 + 4x

Solving for variable 'x'.

Reorder the terms:
-6 + 6x + -4x + -2x2 = 6 + 4x + -6 + -4x

Combine like terms: 6x + -4x = 2x
-6 + 2x + -2x2 = 6 + 4x + -6 + -4x

Reorder the terms:
-6 + 2x + -2x2 = 6 + -6 + 4x + -4x

Combine like terms: 6 + -6 = 0
-6 + 2x + -2x2 = 0 + 4x + -4x
-6 + 2x + -2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-6 + 2x + -2x2 = 0

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

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

Simplifying
-3 + x + -1x2 = 0

Solving
-3 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -1x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -1x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x + x2 = 0 + -3
-1x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x + x2 = -3

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.
-1x + 0.25 + x2 = -3 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + -1x + x2 = -2.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.75

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.