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

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

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

Reorder the terms:
6 + x + 2x + -3x + -1x2 = 0

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

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

Solving
6 + -1x2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

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

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

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}