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

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

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

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

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

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

Solving
1x + 2x2 = 6 + x

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
-3 + x2 = 0

Solving
-3 + x2 = 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 + x2 = 0 + 3

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

Combine like terms: 0 + 3 = 3
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}