(5q+1)(q+1)=0

Solution for (5q+1)(q+1)=0 equation:

Simplifying
(5q + 1)(q + 1) = 0

Reorder the terms:
(1 + 5q)(q + 1) = 0

Reorder the terms:
(1 + 5q)(1 + q) = 0

Multiply (1 + 5q) * (1 + q)
(1(1 + q) + 5q * (1 + q)) = 0
((1 * 1 + q * 1) + 5q * (1 + q)) = 0
((1 + 1q) + 5q * (1 + q)) = 0
(1 + 1q + (1 * 5q + q * 5q)) = 0
(1 + 1q + (5q + 5q2)) = 0

Combine like terms: 1q + 5q = 6q
(1 + 6q + 5q2) = 0

Solving
1 + 6q + 5q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + q)(1 + 5q) = 0

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

Simplifying
1 + q = 0

Solving
1 + q = 0

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

Add '-1' to each side of the equation.
1 + -1 + q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + q = 0 + -1
q = 0 + -1

Combine like terms: 0 + -1 = -1
q = -1

Simplifying
q = -1
Subproblem 2
Set the factor '(1 + 5q)' equal to zero and attempt to solve:

Simplifying
1 + 5q = 0

Solving
1 + 5q = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5q = 0 + -1

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

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

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

Simplifying
q = -0.2
Solution
q = {-1, -0.2}