(x+4)(5x+1)=-14

Solution for (x+4)(5x+1)=-14 equation:

Simplifying
(x + 4)(5x + 1) = -14

Reorder the terms:
(4 + x)(5x + 1) = -14

Reorder the terms:
(4 + x)(1 + 5x) = -14

Multiply (4 + x) * (1 + 5x)
(4(1 + 5x) + x(1 + 5x)) = -14
((1 * 4 + 5x * 4) + x(1 + 5x)) = -14
((4 + 20x) + x(1 + 5x)) = -14
(4 + 20x + (1 * x + 5x * x)) = -14
(4 + 20x + (1x + 5x2)) = -14

Combine like terms: 20x + 1x = 21x
(4 + 21x + 5x2) = -14

Solving
4 + 21x + 5x2 = -14

Solving for variable 'x'.

Reorder the terms:
4 + 14 + 21x + 5x2 = -14 + 14

Combine like terms: 4 + 14 = 18
18 + 21x + 5x2 = -14 + 14

Combine like terms: -14 + 14 = 0
18 + 21x + 5x2 = 0

Factor a trinomial.
(3 + x)(6 + 5x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
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 = {-3, -1.2}