3x+6(4x+6)+4(x^2-2)=

Solution for 3x+6(4x+6)+4(x^2-2)= equation:

Simplifying
3x + 6(4x + 6) + 4(x2 + -2) = 0

Reorder the terms:
3x + 6(6 + 4x) + 4(x2 + -2) = 0
3x + (6 * 6 + 4x * 6) + 4(x2 + -2) = 0
3x + (36 + 24x) + 4(x2 + -2) = 0

Reorder the terms:
3x + 36 + 24x + 4(-2 + x2) = 0
3x + 36 + 24x + (-2 * 4 + x2 * 4) = 0
3x + 36 + 24x + (-8 + 4x2) = 0

Reorder the terms:
36 + -8 + 3x + 24x + 4x2 = 0

Combine like terms: 36 + -8 = 28
28 + 3x + 24x + 4x2 = 0

Combine like terms: 3x + 24x = 27x
28 + 27x + 4x2 = 0

Solving
28 + 27x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
7 + 6.75x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6.75x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 6.75x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6.75x + x2 = 0 + -7
6.75x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
6.75x + x2 = -7

The x term is 6.75x.  Take half its coefficient (3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
6.75x + 11.390625 + x2 = -7 + 11.390625

Reorder the terms:
11.390625 + 6.75x + x2 = -7 + 11.390625

Combine like terms: -7 + 11.390625 = 4.390625
11.390625 + 6.75x + x2 = 4.390625

Factor a perfect square on the left side:
(x + 3.375)(x + 3.375) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(x + 3.375) equal to 2.095381827 and -2.095381827.

Subproblem 1
x + 3.375 = 2.095381827

Simplifying
x + 3.375 = 2.095381827

Reorder the terms:
3.375 + x = 2.095381827

Solving
3.375 + x = 2.095381827

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = 2.095381827 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = 2.095381827 + -3.375
x = 2.095381827 + -3.375

Combine like terms: 2.095381827 + -3.375 = -1.279618173
x = -1.279618173

Simplifying
x = -1.279618173

Subproblem 2
x + 3.375 = -2.095381827

Simplifying
x + 3.375 = -2.095381827

Reorder the terms:
3.375 + x = -2.095381827

Solving
3.375 + x = -2.095381827

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = -2.095381827 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = -2.095381827 + -3.375
x = -2.095381827 + -3.375

Combine like terms: -2.095381827 + -3.375 = -5.470381827
x = -5.470381827

Simplifying
x = -5.470381827

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.279618173, -5.470381827}