(3+x)(2+x)=56

Solution for (3+x)(2+x)=56 equation:

Simplifying
(3 + x)(2 + x) = 56

Multiply (3 + x) * (2 + x)
(3(2 + x) + x(2 + x)) = 56
((2 * 3 + x * 3) + x(2 + x)) = 56
((6 + 3x) + x(2 + x)) = 56
(6 + 3x + (2 * x + x * x)) = 56
(6 + 3x + (2x + x2)) = 56

Combine like terms: 3x + 2x = 5x
(6 + 5x + x2) = 56

Solving
6 + 5x + x2 = 56

Solving for variable 'x'.

Reorder the terms:
6 + -56 + 5x + x2 = 56 + -56

Combine like terms: 6 + -56 = -50
-50 + 5x + x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-50 + 5x + x2 = 0

Factor a trinomial.
(-10 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-10, 5}