3x+46=-4x(x+6)

Solution for 3x+46=-4x(x+6) equation:

Simplifying
3x + 46 = -4x(x + 6)

Reorder the terms:
46 + 3x = -4x(x + 6)

Reorder the terms:
46 + 3x = -4x(6 + x)
46 + 3x = (6 * -4x + x * -4x)
46 + 3x = (-24x + -4x2)

Solving
46 + 3x = -24x + -4x2

Solving for variable 'x'.

Combine like terms: 3x + 24x = 27x
46 + 27x + 4x2 = -24x + -4x2 + 24x + 4x2

Reorder the terms:
46 + 27x + 4x2 = -24x + 24x + -4x2 + 4x2

Combine like terms: -24x + 24x = 0
46 + 27x + 4x2 = 0 + -4x2 + 4x2
46 + 27x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
46 + 27x + 4x2 = 0

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

Divide each side by '4'.
11.5 + 6.75x + x2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + 6.75x + -11.5 + x2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + 6.75x + x2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + 6.75x + x2 = 0 + -11.5
6.75x + x2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
6.75x + x2 = -11.5

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 = -11.5 + 11.390625

Reorder the terms:
11.390625 + 6.75x + x2 = -11.5 + 11.390625

Combine like terms: -11.5 + 11.390625 = -0.109375
11.390625 + 6.75x + x2 = -0.109375

Factor a perfect square on the left side:
(x + 3.375)(x + 3.375) = -0.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.