3x(4+x)=2(3x-8)

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Solution for 3x(4+x)=2(3x-8) equation: 


Simplifying
3x(4 + x) = 2(3x + -8)
(4 * 3x + x * 3x) = 2(3x + -8)
(12x + 3x2) = 2(3x + -8)

Reorder the terms:
12x + 3x2 = 2(-8 + 3x)
12x + 3x2 = (-8 * 2 + 3x * 2)
12x + 3x2 = (-16 + 6x)

Solving
12x + 3x2 = -16 + 6x

Solving for variable 'x'.

Reorder the terms:
16 + 12x + -6x + 3x2 = -16 + 6x + 16 + -6x

Combine like terms: 12x + -6x = 6x
16 + 6x + 3x2 = -16 + 6x + 16 + -6x

Reorder the terms:
16 + 6x + 3x2 = -16 + 16 + 6x + -6x

Combine like terms: -16 + 16 = 0
16 + 6x + 3x2 = 0 + 6x + -6x
16 + 6x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
16 + 6x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + 2x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + 2x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + -5.333333333
2x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
2x + x2 = -5.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -5.333333333 + 1

Reorder the terms:
1 + 2x + x2 = -5.333333333 + 1

Combine like terms: -5.333333333 + 1 = -4.333333333
1 + 2x + x2 = -4.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = -4.333333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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