(7x+1)(5+x)=0

Solution for (7x+1)(5+x)=0 equation:

Simplifying
(7x + 1)(5 + x) = 0

Reorder the terms:
(1 + 7x)(5 + x) = 0

Multiply (1 + 7x) * (5 + x)
(1(5 + x) + 7x * (5 + x)) = 0
((5 * 1 + x * 1) + 7x * (5 + x)) = 0
((5 + 1x) + 7x * (5 + x)) = 0
(5 + 1x + (5 * 7x + x * 7x)) = 0
(5 + 1x + (35x + 7x2)) = 0

Combine like terms: 1x + 35x = 36x
(5 + 36x + 7x2) = 0

Solving
5 + 36x + 7x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {-5, -0.1428571429}