(n-9)(4n+1)=0

Solution for (n-9)(4n+1)=0 equation:

Simplifying
(n + -9)(4n + 1) = 0

Reorder the terms:
(-9 + n)(4n + 1) = 0

Reorder the terms:
(-9 + n)(1 + 4n) = 0

Multiply (-9 + n) * (1 + 4n)
(-9(1 + 4n) + n(1 + 4n)) = 0
((1 * -9 + 4n * -9) + n(1 + 4n)) = 0
((-9 + -36n) + n(1 + 4n)) = 0
(-9 + -36n + (1 * n + 4n * n)) = 0
(-9 + -36n + (1n + 4n2)) = 0

Combine like terms: -36n + 1n = -35n
(-9 + -35n + 4n2) = 0

Solving
-9 + -35n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -4n)(9 + -1n) = 0

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

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4n = 0 + 1

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

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

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

Simplifying
n = -0.25
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-0.25, 9}