3x+x=6-x*2x

Solution for 3x+x=6-x*2x equation:

Simplifying
3x + x = 6 + -1x * 2x

Combine like terms: 3x + x = 4x
4x = 6 + -1x * 2x

Reorder the terms for easier multiplication:
4x = 6 + -1 * 2x * x

Multiply -1 * 2
4x = 6 + -2x * x

Multiply x * x
4x = 6 + -2x2

Solving
4x = 6 + -2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-3, 1}