-2x(x+2)+3x=14

Solution for -2x(x+2)+3x=14 equation:

Simplifying
-2x(x + 2) + 3x = 14

Reorder the terms:
-2x(2 + x) + 3x = 14
(2 * -2x + x * -2x) + 3x = 14
(-4x + -2x2) + 3x = 14

Reorder the terms:
-4x + 3x + -2x2 = 14

Combine like terms: -4x + 3x = -1x
-1x + -2x2 = 14

Solving
-1x + -2x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + -1x + -2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -1x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(14 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
14 + x + 2x2 = 0

Solving
14 + x + 2x2 = 0

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

Divide each side by '2'.
7 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 0.5x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 0.5x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 0.5x + x2 = 0 + -7
0.5x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
0.5x + x2 = -7

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 = -7 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -7 + 0.25

Combine like terms: -7 + 0.25 = -6.75
0.25 + 0.5x + x2 = -6.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -6.75

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.