(6x+1)(x+3)=0

Solution for (6x+1)(x+3)=0 equation:

Simplifying
(6x + 1)(x + 3) = 0

Reorder the terms:
(1 + 6x)(x + 3) = 0

Reorder the terms:
(1 + 6x)(3 + x) = 0

Multiply (1 + 6x) * (3 + x)
(1(3 + x) + 6x * (3 + x)) = 0
((3 * 1 + x * 1) + 6x * (3 + x)) = 0
((3 + 1x) + 6x * (3 + x)) = 0
(3 + 1x + (3 * 6x + x * 6x)) = 0
(3 + 1x + (18x + 6x2)) = 0

Combine like terms: 1x + 18x = 19x
(3 + 19x + 6x2) = 0

Solving
3 + 19x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + x)(1 + 6x) = 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 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x = 0 + -1
6x = 0 + -1

Combine like terms: 0 + -1 = -1
6x = -1

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Solution
x = {-3, -0.1666666667}