(X+2)(X+3)=30

Solution for (X+2)(X+3)=30 equation:

Simplifying
(X + 2)(X + 3) = 30

Reorder the terms:
(2 + X)(X + 3) = 30

Reorder the terms:
(2 + X)(3 + X) = 30

Multiply (2 + X) * (3 + X)
(2(3 + X) + X(3 + X)) = 30
((3 * 2 + X * 2) + X(3 + X)) = 30
((6 + 2X) + X(3 + X)) = 30
(6 + 2X + (3 * X + X * X)) = 30
(6 + 2X + (3X + X2)) = 30

Combine like terms: 2X + 3X = 5X
(6 + 5X + X2) = 30

Solving
6 + 5X + X2 = 30

Solving for variable 'X'.

Reorder the terms:
6 + -30 + 5X + X2 = 30 + -30

Combine like terms: 6 + -30 = -24
-24 + 5X + X2 = 30 + -30

Combine like terms: 30 + -30 = 0
-24 + 5X + X2 = 0

Factor a trinomial.
(-8 + -1X)(3 + -1X) = 0

Subproblem 1
Set the factor '(-8 + -1X)' equal to zero and attempt to solve:

Simplifying
-8 + -1X = 0

Solving
-8 + -1X = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1X = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1X = 0 + 8
-1X = 0 + 8

Combine like terms: 0 + 8 = 8
-1X = 8

Divide each side by '-1'.
X = -8

Simplifying
X = -8
Subproblem 2
Set the factor '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1X = 0 + -3
-1X = 0 + -3

Combine like terms: 0 + -3 = -3
-1X = -3

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Solution
X = {-8, 3}