2(x^2+1)+2(x^2+6x)+3=0

Solution for 2(x^2+1)+2(x^2+6x)+3=0 equation:

Simplifying
2(x2 + 1) + 2(x2 + 6x) + 3 = 0

Reorder the terms:
2(1 + x2) + 2(x2 + 6x) + 3 = 0
(1 * 2 + x2 * 2) + 2(x2 + 6x) + 3 = 0
(2 + 2x2) + 2(x2 + 6x) + 3 = 0

Reorder the terms:
2 + 2x2 + 2(6x + x2) + 3 = 0
2 + 2x2 + (6x * 2 + x2 * 2) + 3 = 0
2 + 2x2 + (12x + 2x2) + 3 = 0

Reorder the terms:
2 + 3 + 12x + 2x2 + 2x2 = 0

Combine like terms: 2 + 3 = 5
5 + 12x + 2x2 + 2x2 = 0

Combine like terms: 2x2 + 2x2 = 4x2
5 + 12x + 4x2 = 0

Solving
5 + 12x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + 2x)(1 + 2x) = 0

Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2.5, -0.5}