(x+5)(5x+1)=-19

Solution for (x+5)(5x+1)=-19 equation:

Simplifying
(x + 5)(5x + 1) = -19

Reorder the terms:
(5 + x)(5x + 1) = -19

Reorder the terms:
(5 + x)(1 + 5x) = -19

Multiply (5 + x) * (1 + 5x)
(5(1 + 5x) + x(1 + 5x)) = -19
((1 * 5 + 5x * 5) + x(1 + 5x)) = -19
((5 + 25x) + x(1 + 5x)) = -19
(5 + 25x + (1 * x + 5x * x)) = -19
(5 + 25x + (1x + 5x2)) = -19

Combine like terms: 25x + 1x = 26x
(5 + 26x + 5x2) = -19

Solving
5 + 26x + 5x2 = -19

Solving for variable 'x'.

Reorder the terms:
5 + 19 + 26x + 5x2 = -19 + 19

Combine like terms: 5 + 19 = 24
24 + 26x + 5x2 = -19 + 19

Combine like terms: -19 + 19 = 0
24 + 26x + 5x2 = 0

Factor a trinomial.
(4 + x)(6 + 5x) = 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 '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Solution
x = {-4, -1.2}