(x+5)(4x+1)=-15

Solution for (x+5)(4x+1)=-15 equation:

Simplifying
(x + 5)(4x + 1) = -15

Reorder the terms:
(5 + x)(4x + 1) = -15

Reorder the terms:
(5 + x)(1 + 4x) = -15

Multiply (5 + x) * (1 + 4x)
(5(1 + 4x) + x(1 + 4x)) = -15
((1 * 5 + 4x * 5) + x(1 + 4x)) = -15
((5 + 20x) + x(1 + 4x)) = -15
(5 + 20x + (1 * x + 4x * x)) = -15
(5 + 20x + (1x + 4x2)) = -15

Combine like terms: 20x + 1x = 21x
(5 + 21x + 4x2) = -15

Solving
5 + 21x + 4x2 = -15

Solving for variable 'x'.

Reorder the terms:
5 + 15 + 21x + 4x2 = -15 + 15

Combine like terms: 5 + 15 = 20
20 + 21x + 4x2 = -15 + 15

Combine like terms: -15 + 15 = 0
20 + 21x + 4x2 = 0

Factor a trinomial.
(4 + x)(5 + 4x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 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 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-4, -1.25}