(x+1)(x+2)=30

Solution for (x+1)(x+2)=30 equation:

Simplifying
(x + 1)(x + 2) = 30

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

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

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 30
((2 * 1 + x * 1) + x(2 + x)) = 30
((2 + 1x) + x(2 + x)) = 30
(2 + 1x + (2 * x + x * x)) = 30
(2 + 1x + (2x + x2)) = 30

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 30

Solving
2 + 3x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
2 + -30 + 3x + x2 = 30 + -30

Combine like terms: 2 + -30 = -28
-28 + 3x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-28 + 3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -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 '(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 = {-7, 4}