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

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

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

Reorder the terms:
3x(4 + x) + -2x + 6 = 3x + 2 + -4(x + 3)
(4 * 3x + x * 3x) + -2x + 6 = 3x + 2 + -4(x + 3)
(12x + 3x2) + -2x + 6 = 3x + 2 + -4(x + 3)

Reorder the terms:
6 + 12x + -2x + 3x2 = 3x + 2 + -4(x + 3)

Combine like terms: 12x + -2x = 10x
6 + 10x + 3x2 = 3x + 2 + -4(x + 3)

Reorder the terms:
6 + 10x + 3x2 = 3x + 2 + -4(3 + x)
6 + 10x + 3x2 = 3x + 2 + (3 * -4 + x * -4)
6 + 10x + 3x2 = 3x + 2 + (-12 + -4x)

Reorder the terms:
6 + 10x + 3x2 = 2 + -12 + 3x + -4x

Combine like terms: 2 + -12 = -10
6 + 10x + 3x2 = -10 + 3x + -4x

Combine like terms: 3x + -4x = -1x
6 + 10x + 3x2 = -10 + -1x

Solving
6 + 10x + 3x2 = -10 + -1x

Solving for variable 'x'.

Reorder the terms:
6 + 10 + 10x + x + 3x2 = -10 + -1x + 10 + x

Combine like terms: 6 + 10 = 16
16 + 10x + x + 3x2 = -10 + -1x + 10 + x

Combine like terms: 10x + x = 11x
16 + 11x + 3x2 = -10 + -1x + 10 + x

Reorder the terms:
16 + 11x + 3x2 = -10 + 10 + -1x + x

Combine like terms: -10 + 10 = 0
16 + 11x + 3x2 = 0 + -1x + x
16 + 11x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
16 + 11x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + 3.666666667x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + 3.666666667x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + 3.666666667x + x2 = 0 + -5.333333333
3.666666667x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
3.666666667x + x2 = -5.333333333

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = -5.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = -5.333333333 + 3.361111114

Combine like terms: -5.333333333 + 3.361111114 = -1.972222219
3.361111114 + 3.666666667x + x2 = -1.972222219

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = -1.972222219

Can't calculate square root of the right side.

The solution to this equation could not be determined.