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

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

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

Remove parenthesis around (-3x)
-3x(x + 2) = 4

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

Solving
-6x + -3x2 = 4

Solving for variable 'x'.

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

Combine like terms: 4 + -4 = 0
-4 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 6x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 6x + 3x2 = 0

Solving
4 + 6x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 2x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 2x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + -1.333333333
2x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
2x + x2 = -1.333333333

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 = -1.333333333 + 1

Reorder the terms:
1 + 2x + x2 = -1.333333333 + 1

Combine like terms: -1.333333333 + 1 = -0.333333333
1 + 2x + x2 = -0.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = -0.333333333

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.