(x+2)*(3+2x)=1

Solution for (x+2)*(3+2x)=1 equation:

Simplifying
(x + 2)(3 + 2x) = 1

Reorder the terms:
(2 + x)(3 + 2x) = 1

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) = 1
((3 * 2 + 2x * 2) + x(3 + 2x)) = 1
((6 + 4x) + x(3 + 2x)) = 1
(6 + 4x + (3 * x + 2x * x)) = 1
(6 + 4x + (3x + 2x2)) = 1

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) = 1

Solving
6 + 7x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
6 + -1 + 7x + 2x2 = 1 + -1

Combine like terms: 6 + -1 = 5
5 + 7x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
5 + 7x + 2x2 = 0

Factor a trinomial.
(5 + 2x)(1 + x) = 0

Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-2.5, -1}