(x+7)(x+1)=55

Solution for (x+7)(x+1)=55 equation:

Simplifying
(x + 7)(x + 1) = 55

Reorder the terms:
(7 + x)(x + 1) = 55

Reorder the terms:
(7 + x)(1 + x) = 55

Multiply (7 + x) * (1 + x)
(7(1 + x) + x(1 + x)) = 55
((1 * 7 + x * 7) + x(1 + x)) = 55
((7 + 7x) + x(1 + x)) = 55
(7 + 7x + (1 * x + x * x)) = 55
(7 + 7x + (1x + x2)) = 55

Combine like terms: 7x + 1x = 8x
(7 + 8x + x2) = 55

Solving
7 + 8x + x2 = 55

Solving for variable 'x'.

Reorder the terms:
7 + -55 + 8x + x2 = 55 + -55

Combine like terms: 7 + -55 = -48
-48 + 8x + x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-48 + 8x + x2 = 0

Factor a trinomial.
(-12 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-12, 4}