6(x+1)(x+1)+4x(x+1)-12=0

Solution for 6(x+1)(x+1)+4x(x+1)-12=0 equation:

Simplifying
6(x + 1)(x + 1) + 4x(x + 1) + -12 = 0

Reorder the terms:
6(1 + x)(x + 1) + 4x(x + 1) + -12 = 0

Reorder the terms:
6(1 + x)(1 + x) + 4x(x + 1) + -12 = 0

Multiply (1 + x) * (1 + x)
6(1(1 + x) + x(1 + x)) + 4x(x + 1) + -12 = 0
6((1 * 1 + x * 1) + x(1 + x)) + 4x(x + 1) + -12 = 0
6((1 + 1x) + x(1 + x)) + 4x(x + 1) + -12 = 0
6(1 + 1x + (1 * x + x * x)) + 4x(x + 1) + -12 = 0
6(1 + 1x + (1x + x2)) + 4x(x + 1) + -12 = 0

Combine like terms: 1x + 1x = 2x
6(1 + 2x + x2) + 4x(x + 1) + -12 = 0
(1 * 6 + 2x * 6 + x2 * 6) + 4x(x + 1) + -12 = 0
(6 + 12x + 6x2) + 4x(x + 1) + -12 = 0

Reorder the terms:
6 + 12x + 6x2 + 4x(1 + x) + -12 = 0
6 + 12x + 6x2 + (1 * 4x + x * 4x) + -12 = 0
6 + 12x + 6x2 + (4x + 4x2) + -12 = 0

Reorder the terms:
6 + -12 + 12x + 4x + 6x2 + 4x2 = 0

Combine like terms: 6 + -12 = -6
-6 + 12x + 4x + 6x2 + 4x2 = 0

Combine like terms: 12x + 4x = 16x
-6 + 16x + 6x2 + 4x2 = 0

Combine like terms: 6x2 + 4x2 = 10x2
-6 + 16x + 10x2 = 0

Solving
-6 + 16x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 8x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 8x + 5x2)' equal to zero and attempt to solve:

Simplifying
-3 + 8x + 5x2 = 0

Solving
-3 + 8x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 1.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 1.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 1.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 1.6x + x2 = 0 + 0.6
1.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
1.6x + x2 = 0.6

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.6 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.6 + 0.64

Combine like terms: 0.6 + 0.64 = 1.24
0.64 + 1.6x + x2 = 1.24

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.113552873 and -1.113552873.

Subproblem 1
x + 0.8 = 1.113552873

Simplifying
x + 0.8 = 1.113552873

Reorder the terms:
0.8 + x = 1.113552873

Solving
0.8 + x = 1.113552873

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 1.113552873 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 1.113552873 + -0.8
x = 1.113552873 + -0.8

Combine like terms: 1.113552873 + -0.8 = 0.313552873
x = 0.313552873

Simplifying
x = 0.313552873

Subproblem 2
x + 0.8 = -1.113552873

Simplifying
x + 0.8 = -1.113552873

Reorder the terms:
0.8 + x = -1.113552873

Solving
0.8 + x = -1.113552873

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -1.113552873 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -1.113552873 + -0.8
x = -1.113552873 + -0.8

Combine like terms: -1.113552873 + -0.8 = -1.913552873
x = -1.913552873

Simplifying
x = -1.913552873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.313552873, -1.913552873}
Solution
x = {0.313552873, -1.913552873}