(x+1)(x+7)=

Solution for (x+1)(x+7)= equation:

Simplifying
(x + 1)(x + 7) = 0

Reorder the terms:
(1 + x)(x + 7) = 0

Reorder the terms:
(1 + x)(7 + x) = 0

Multiply (1 + x) * (7 + x)
(1(7 + x) + x(7 + x)) = 0
((7 * 1 + x * 1) + x(7 + x)) = 0
((7 + 1x) + x(7 + x)) = 0
(7 + 1x + (7 * x + x * x)) = 0
(7 + 1x + (7x + x2)) = 0

Combine like terms: 1x + 7x = 8x
(7 + 8x + x2) = 0

Solving
7 + 8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + x)(1 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
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 = {-7, -1}