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

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

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

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

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

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

Combine like terms: -3x + 2x = -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.
(-4 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-4, 5}