(X+8)(X+2)=7

Solution for (X+8)(X+2)=7 equation:

Simplifying
(X + 8)(X + 2) = 7

Reorder the terms:
(8 + X)(X + 2) = 7

Reorder the terms:
(8 + X)(2 + X) = 7

Multiply (8 + X) * (2 + X)
(8(2 + X) + X(2 + X)) = 7
((2 * 8 + X * 8) + X(2 + X)) = 7
((16 + 8X) + X(2 + X)) = 7
(16 + 8X + (2 * X + X * X)) = 7
(16 + 8X + (2X + X2)) = 7

Combine like terms: 8X + 2X = 10X
(16 + 10X + X2) = 7

Solving
16 + 10X + X2 = 7

Solving for variable 'X'.

Reorder the terms:
16 + -7 + 10X + X2 = 7 + -7

Combine like terms: 16 + -7 = 9
9 + 10X + X2 = 7 + -7

Combine like terms: 7 + -7 = 0
9 + 10X + X2 = 0

Factor a trinomial.
(9 + X)(1 + X) = 0

Subproblem 1
Set the factor '(9 + X)' equal to zero and attempt to solve:

Simplifying
9 + X = 0

Solving
9 + X = 0

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

Add '-9' to each side of the equation.
9 + -9 + X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + X = 0 + -9
X = 0 + -9

Combine like terms: 0 + -9 = -9
X = -9

Simplifying
X = -9
Subproblem 2
Set the factor '(1 + X)' equal to zero and attempt to solve:

Simplifying
1 + X = 0

Solving
1 + X = 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 + X = 0 + -1

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

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

Simplifying
X = -1
Solution
X = {-9, -1}