3x(x+2)=6-x

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

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

Reorder the terms:
3x(2 + x) = 6 + -1x
(2 * 3x + x * 3x) = 6 + -1x
(6x + 3x2) = 6 + -1x

Solving
6x + 3x2 = 6 + -1x

Solving for variable 'x'.

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

Combine like terms: 6x + x = 7x
-6 + 7x + 3x2 = 6 + -1x + -6 + x

Reorder the terms:
-6 + 7x + 3x2 = 6 + -6 + -1x + x

Combine like terms: 6 + -6 = 0
-6 + 7x + 3x2 = 0 + -1x + x
-6 + 7x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
-6 + 7x + 3x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -3x) = 0

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-3, 0.6666666667}