((2x^2)+1x)+(6x+6)=0

Solution for ((2x^2)+1x)+(6x+6)=0 equation:

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

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

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

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

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

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

Combine like terms: 1x + 6x = 7x
6 + 7x + (2x2) = 0

Solving
6 + 7x + (2x2) = 0

Solving for variable 'x'.

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

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

Simplifying
2 + x = 0

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

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

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-2, -1.5}