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

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

Simplifying
(3 + x)(2 + -1x) = 14

Multiply (3 + x) * (2 + -1x)
(3(2 + -1x) + x(2 + -1x)) = 14
((2 * 3 + -1x * 3) + x(2 + -1x)) = 14
((6 + -3x) + x(2 + -1x)) = 14
(6 + -3x + (2 * x + -1x * x)) = 14
(6 + -3x + (2x + -1x2)) = 14

Combine like terms: -3x + 2x = -1x
(6 + -1x + -1x2) = 14

Solving
6 + -1x + -1x2 = 14

Solving for variable 'x'.

Reorder the terms:
6 + -14 + -1x + -1x2 = 14 + -14

Combine like terms: 6 + -14 = -8
-8 + -1x + -1x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-8 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + x + x2)' equal to zero and attempt to solve:

Simplifying
8 + x + x2 = 0

Solving
8 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x + x2 = 0 + -8
x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
x + x2 = -8

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.
x + 0.25 + x2 = -8 + 0.25

Reorder the terms:
0.25 + x + x2 = -8 + 0.25

Combine like terms: -8 + 0.25 = -7.75
0.25 + x + x2 = -7.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -7.75

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.