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

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

Simplifying
(2 + x)(2x + 3) = 0

Reorder the terms:
(2 + x)(3 + 2x) = 0

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) = 0
((3 * 2 + 2x * 2) + x(3 + 2x)) = 0
((6 + 4x) + x(3 + 2x)) = 0
(6 + 4x + (3 * x + 2x * x)) = 0
(6 + 4x + (3x + 2x2)) = 0

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) = 0

Solving
6 + 7x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + x)(3 + 2x) = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-2, -1.5}