3x+(x+4)+8=(x+3)(x+2)

Solution for 3x+(x+4)+8=(x+3)(x+2) equation:

Simplifying
3x + (x + 4) + 8 = (x + 3)(x + 2)

Reorder the terms:
3x + (4 + x) + 8 = (x + 3)(x + 2)

Remove parenthesis around (4 + x)
3x + 4 + x + 8 = (x + 3)(x + 2)

Reorder the terms:
4 + 8 + 3x + x = (x + 3)(x + 2)

Combine like terms: 4 + 8 = 12
12 + 3x + x = (x + 3)(x + 2)

Combine like terms: 3x + x = 4x
12 + 4x = (x + 3)(x + 2)

Reorder the terms:
12 + 4x = (3 + x)(x + 2)

Reorder the terms:
12 + 4x = (3 + x)(2 + x)

Multiply (3 + x) * (2 + x)
12 + 4x = (3(2 + x) + x(2 + x))
12 + 4x = ((2 * 3 + x * 3) + x(2 + x))
12 + 4x = ((6 + 3x) + x(2 + x))
12 + 4x = (6 + 3x + (2 * x + x * x))
12 + 4x = (6 + 3x + (2x + x2))

Combine like terms: 3x + 2x = 5x
12 + 4x = (6 + 5x + x2)

Solving
12 + 4x = 6 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
12 + -6 + 4x + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2

Combine like terms: 12 + -6 = 6
6 + 4x + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2

Combine like terms: 4x + -5x = -1x
6 + -1x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2

Reorder the terms:
6 + -1x + -1x2 = 6 + -6 + 5x + -5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
6 + -1x + -1x2 = 0 + 5x + -5x + x2 + -1x2
6 + -1x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
6 + -1x + -1x2 = 0 + x2 + -1x2
6 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -1x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(3 + x) = 0

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {2, -3}