(x+3)(2x+3)=5

Solution for (x+3)(2x+3)=5 equation:

Simplifying
(x + 3)(2x + 3) = 5

Reorder the terms:
(3 + x)(2x + 3) = 5

Reorder the terms:
(3 + x)(3 + 2x) = 5

Multiply (3 + x) * (3 + 2x)
(3(3 + 2x) + x(3 + 2x)) = 5
((3 * 3 + 2x * 3) + x(3 + 2x)) = 5
((9 + 6x) + x(3 + 2x)) = 5
(9 + 6x + (3 * x + 2x * x)) = 5
(9 + 6x + (3x + 2x2)) = 5

Combine like terms: 6x + 3x = 9x
(9 + 9x + 2x2) = 5

Solving
9 + 9x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
9 + -5 + 9x + 2x2 = 5 + -5

Combine like terms: 9 + -5 = 4
4 + 9x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
4 + 9x + 2x2 = 0

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

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-4, -0.5}