(X+2)(X+3)-20=0

Solution for (X+2)(X+3)-20=0 equation:

Simplifying
(X + 2)(X + 3) + -20 = 0

Reorder the terms:
(2 + X)(X + 3) + -20 = 0

Reorder the terms:
(2 + X)(3 + X) + -20 = 0

Multiply (2 + X) * (3 + X)
(2(3 + X) + X(3 + X)) + -20 = 0
((3 * 2 + X * 2) + X(3 + X)) + -20 = 0
((6 + 2X) + X(3 + X)) + -20 = 0
(6 + 2X + (3 * X + X * X)) + -20 = 0
(6 + 2X + (3X + X2)) + -20 = 0

Combine like terms: 2X + 3X = 5X
(6 + 5X + X2) + -20 = 0

Reorder the terms:
6 + -20 + 5X + X2 = 0

Combine like terms: 6 + -20 = -14
-14 + 5X + X2 = 0

Solving
-14 + 5X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-7 + -1X)(2 + -1X) = 0

Subproblem 1
Set the factor '(-7 + -1X)' equal to zero and attempt to solve:

Simplifying
-7 + -1X = 0

Solving
-7 + -1X = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1X = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1X = 0 + 7
-1X = 0 + 7

Combine like terms: 0 + 7 = 7
-1X = 7

Divide each side by '-1'.
X = -7

Simplifying
X = -7
Subproblem 2
Set the factor '(2 + -1X)' equal to zero and attempt to solve:

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Solution
X = {-7, 2}