(10+x)*(2+x)=105

Solution for (10+x)*(2+x)=105 equation:

Simplifying
(10 + x)(2 + x) = 105

Multiply (10 + x) * (2 + x)
(10(2 + x) + x(2 + x)) = 105
((2 * 10 + x * 10) + x(2 + x)) = 105
((20 + 10x) + x(2 + x)) = 105
(20 + 10x + (2 * x + x * x)) = 105
(20 + 10x + (2x + x2)) = 105

Combine like terms: 10x + 2x = 12x
(20 + 12x + x2) = 105

Solving
20 + 12x + x2 = 105

Solving for variable 'x'.

Reorder the terms:
20 + -105 + 12x + x2 = 105 + -105

Combine like terms: 20 + -105 = -85
-85 + 12x + x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-85 + 12x + x2 = 0

Factor a trinomial.
(-17 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
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 = {-17, 5}