(x^2+x+6)-(8x-2x)=

Solution for (x^2+x+6)-(8x-2x)= equation:

Simplifying
(x2 + x + 6) + -1(8x + -2x) = 0

Reorder the terms:
(6 + x + x2) + -1(8x + -2x) = 0

Remove parenthesis around (6 + x + x2)
6 + x + x2 + -1(8x + -2x) = 0

Combine like terms: 8x + -2x = 6x
6 + x + x2 + -1(6x) = 0

Remove parenthesis around (6x)
6 + x + x2 + -1 * 6x = 0

Multiply -1 * 6
6 + x + x2 + -6x = 0

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

Combine like terms: x + -6x = -5x
6 + -5x + x2 = 0

Solving
6 + -5x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, 3}