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

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

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

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

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

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

Solving
-6 + 1x + x2 = 14

Solving for variable 'x'.

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

Combine like terms: -6 + -14 = -20
-20 + 1x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-20 + 1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}