2[x(4+2x)+3]=2x+2

Solution for 2[x(4+2x)+3]=2x+2 equation:

Simplifying
2[x(4 + 2x) + 3] = 2x + 2
2[(4 * x + 2x * x) + 3] = 2x + 2
2[(4x + 2x2) + 3] = 2x + 2

Reorder the terms:
2[3 + 4x + 2x2] = 2x + 2
[3 * 2 + 4x * 2 + 2x2 * 2] = 2x + 2
[6 + 8x + 4x2] = 2x + 2

Reorder the terms:
6 + 8x + 4x2 = 2 + 2x

Solving
6 + 8x + 4x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
6 + -2 + 8x + -2x + 4x2 = 2 + 2x + -2 + -2x

Combine like terms: 6 + -2 = 4
4 + 8x + -2x + 4x2 = 2 + 2x + -2 + -2x

Combine like terms: 8x + -2x = 6x
4 + 6x + 4x2 = 2 + 2x + -2 + -2x

Reorder the terms:
4 + 6x + 4x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
4 + 6x + 4x2 = 0 + 2x + -2x
4 + 6x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
4 + 6x + 4x2 = 0

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

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

Simplifying
2 + 3x + 2x2 = 0

Solving
2 + 3x + 2x2 = 0

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

Divide each side by '2'.
1 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 1.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.5x + x2 = 0 + -1
1.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.5x + x2 = -1

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -1 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -1 + 0.5625

Combine like terms: -1 + 0.5625 = -0.4375
0.5625 + 1.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -0.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.