(2x+3)(x+2)=10

Solution for (2x+3)(x+2)=10 equation:

Simplifying
(2x + 3)(x + 2) = 10

Reorder the terms:
(3 + 2x)(x + 2) = 10

Reorder the terms:
(3 + 2x)(2 + x) = 10

Multiply (3 + 2x) * (2 + x)
(3(2 + x) + 2x * (2 + x)) = 10
((2 * 3 + x * 3) + 2x * (2 + x)) = 10
((6 + 3x) + 2x * (2 + x)) = 10
(6 + 3x + (2 * 2x + x * 2x)) = 10
(6 + 3x + (4x + 2x2)) = 10

Combine like terms: 3x + 4x = 7x
(6 + 7x + 2x2) = 10

Solving
6 + 7x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
6 + -10 + 7x + 2x2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 7x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 7x + 2x2 = 0

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

Subproblem 1
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
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}