(x+3)(x+2)=30

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

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

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

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

Multiply (3 + x) * (2 + x)
(3(2 + x) + x(2 + x)) = 30
((2 * 3 + x * 3) + x(2 + x)) = 30
((6 + 3x) + x(2 + x)) = 30
(6 + 3x + (2 * x + x * x)) = 30
(6 + 3x + (2x + x2)) = 30

Combine like terms: 3x + 2x = 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}