7x-2x(x+4)=27

Solution for 7x-2x(x+4)=27 equation:

Simplifying
7x + -2x(x + 4) = 27

Reorder the terms:
7x + -2x(4 + x) = 27
7x + (4 * -2x + x * -2x) = 27
7x + (-8x + -2x2) = 27

Combine like terms: 7x + -8x = -1x
-1x + -2x2 = 27

Solving
-1x + -2x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + -1x + -2x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -1x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(27 + x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(27 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
27 + x + 2x2 = 0

Solving
27 + x + 2x2 = 0

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

Divide each side by '2'.
13.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + 0.5x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + 0.5x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + 0.5x + x2 = 0 + -13.5
0.5x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
0.5x + x2 = -13.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = -13.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -13.5 + 0.25

Combine like terms: -13.5 + 0.25 = -13.25
0.25 + 0.5x + x2 = -13.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -13.25

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.