(8+x)(10+x)=99

Solution for (8+x)(10+x)=99 equation:

Simplifying
(8 + x)(10 + x) = 99

Multiply (8 + x) * (10 + x)
(8(10 + x) + x(10 + x)) = 99
((10 * 8 + x * 8) + x(10 + x)) = 99
((80 + 8x) + x(10 + x)) = 99
(80 + 8x + (10 * x + x * x)) = 99
(80 + 8x + (10x + x2)) = 99

Combine like terms: 8x + 10x = 18x
(80 + 18x + x2) = 99

Solving
80 + 18x + x2 = 99

Solving for variable 'x'.

Reorder the terms:
80 + -99 + 18x + x2 = 99 + -99

Combine like terms: 80 + -99 = -19
-19 + 18x + x2 = 99 + -99

Combine like terms: 99 + -99 = 0
-19 + 18x + x2 = 0

Factor a trinomial.
(-19 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-19, 1}