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

Solution for (x+2)(x-3)-x(2x+1)+6x=0 equation:

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

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

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

Multiply (2 + x) * (-3 + x)
(2(-3 + x) + x(-3 + x)) + -1x(2x + 1) + 6x = 0
((-3 * 2 + x * 2) + x(-3 + x)) + -1x(2x + 1) + 6x = 0
((-6 + 2x) + x(-3 + x)) + -1x(2x + 1) + 6x = 0
(-6 + 2x + (-3 * x + x * x)) + -1x(2x + 1) + 6x = 0
(-6 + 2x + (-3x + x2)) + -1x(2x + 1) + 6x = 0

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

Reorder the terms:
-6 + -1x + x2 + -1x(1 + 2x) + 6x = 0
-6 + -1x + x2 + (1 * -1x + 2x * -1x) + 6x = 0
-6 + -1x + x2 + (-1x + -2x2) + 6x = 0

Reorder the terms:
-6 + -1x + -1x + 6x + x2 + -2x2 = 0

Combine like terms: -1x + -1x = -2x
-6 + -2x + 6x + x2 + -2x2 = 0

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

Combine like terms: x2 + -2x2 = -1x2
-6 + 4x + -1x2 = 0

Solving
-6 + 4x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
6 + -4x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -4x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -4x + x2 = 0 + -6

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

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

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -6 + 4

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

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

Factor a perfect square on the left side:
(x + -2)(x + -2) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.