(4x+1)(1x+5)=0

Solution for (4x+1)(1x+5)=0 equation:

Simplifying
(4x + 1)(1x + 5) = 0

Reorder the terms:
(1 + 4x)(1x + 5) = 0

Reorder the terms:
(1 + 4x)(5 + 1x) = 0

Multiply (1 + 4x) * (5 + 1x)
(1(5 + 1x) + 4x * (5 + 1x)) = 0
((5 * 1 + 1x * 1) + 4x * (5 + 1x)) = 0
((5 + 1x) + 4x * (5 + 1x)) = 0
(5 + 1x + (5 * 4x + 1x * 4x)) = 0
(5 + 1x + (20x + 4x2)) = 0

Combine like terms: 1x + 20x = 21x
(5 + 21x + 4x2) = 0

Solving
5 + 21x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(1 + 4x) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-5, -0.25}