(q-5)(4q+1)=0

Solution for (q-5)(4q+1)=0 equation:

Simplifying
(q + -5)(4q + 1) = 0

Reorder the terms:
(-5 + q)(4q + 1) = 0

Reorder the terms:
(-5 + q)(1 + 4q) = 0

Multiply (-5 + q) * (1 + 4q)
(-5(1 + 4q) + q(1 + 4q)) = 0
((1 * -5 + 4q * -5) + q(1 + 4q)) = 0
((-5 + -20q) + q(1 + 4q)) = 0
(-5 + -20q + (1 * q + 4q * q)) = 0
(-5 + -20q + (1q + 4q2)) = 0

Combine like terms: -20q + 1q = -19q
(-5 + -19q + 4q2) = 0

Solving
-5 + -19q + 4q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -4q)(5 + -1q) = 0

Subproblem 1
Set the factor '(-1 + -4q)' equal to zero and attempt to solve:

Simplifying
-1 + -4q = 0

Solving
-1 + -4q = 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 + -4q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4q = 0 + 1
-4q = 0 + 1

Combine like terms: 0 + 1 = 1
-4q = 1

Divide each side by '-4'.
q = -0.25

Simplifying
q = -0.25
Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

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

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

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

Divide each side by '-1'.
q = 5

Simplifying
q = 5
Solution
q = {-0.25, 5}