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

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

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

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

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

Multiply (5 + x) * (-1 + x)
(5(-1 + x) + x(-1 + x)) = 0
((-1 * 5 + x * 5) + x(-1 + x)) = 0
((-5 + 5x) + x(-1 + x)) = 0
(-5 + 5x + (-1 * x + x * x)) = 0
(-5 + 5x + (-1x + x2)) = 0

Combine like terms: 5x + -1x = 4x
(-5 + 4x + x2) = 0

Solving
-5 + 4x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 1}