(x+3)(5x+1)=0

Solution for (x+3)(5x+1)=0 equation:

Simplifying
(x + 3)(5x + 1) = 0

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

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

Multiply (3 + x) * (1 + 5x)
(3(1 + 5x) + x(1 + 5x)) = 0
((1 * 3 + 5x * 3) + x(1 + 5x)) = 0
((3 + 15x) + x(1 + 5x)) = 0
(3 + 15x + (1 * x + 5x * x)) = 0
(3 + 15x + (1x + 5x2)) = 0

Combine like terms: 15x + 1x = 16x
(3 + 16x + 5x2) = 0

Solving
3 + 16x + 5x2 = 0

Solving for variable 'x'.

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

Simplifying
1 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-3, -0.2}