(3+x)(2-x)=12

Solution for (3+x)(2-x)=12 equation:

Simplifying
(3 + x)(2 + -1x) = 12

Multiply (3 + x) * (2 + -1x)
(3(2 + -1x) + x(2 + -1x)) = 12
((2 * 3 + -1x * 3) + x(2 + -1x)) = 12
((6 + -3x) + x(2 + -1x)) = 12
(6 + -3x + (2 * x + -1x * x)) = 12
(6 + -3x + (2x + -1x2)) = 12

Combine like terms: -3x + 2x = -1x
(6 + -1x + -1x2) = 12

Solving
6 + -1x + -1x2 = 12

Solving for variable 'x'.

Reorder the terms:
6 + -12 + -1x + -1x2 = 12 + -12

Combine like terms: 6 + -12 = -6
-6 + -1x + -1x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-6 + -1x + -1x2 = 0

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

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

Simplifying
6 + x + x2 = 0

Solving
6 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + x + x2 = 0 + -6

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

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

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 = -6 + 0.25

Reorder the terms:
0.25 + x + x2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + x + x2 = -5.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -5.75

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.