(4n-7)(n+5)=0

Solution for (4n-7)(n+5)=0 equation:

Simplifying
(4n + -7)(n + 5) = 0

Reorder the terms:
(-7 + 4n)(n + 5) = 0

Reorder the terms:
(-7 + 4n)(5 + n) = 0

Multiply (-7 + 4n) * (5 + n)
(-7(5 + n) + 4n * (5 + n)) = 0
((5 * -7 + n * -7) + 4n * (5 + n)) = 0
((-35 + -7n) + 4n * (5 + n)) = 0
(-35 + -7n + (5 * 4n + n * 4n)) = 0
(-35 + -7n + (20n + 4n2)) = 0

Combine like terms: -7n + 20n = 13n
(-35 + 13n + 4n2) = 0

Solving
-35 + 13n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -1n)(7 + -4n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

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

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

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

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

Simplifying
n = -5
Subproblem 2
Set the factor '(7 + -4n)' equal to zero and attempt to solve:

Simplifying
7 + -4n = 0

Solving
7 + -4n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4n = 0 + -7
-4n = 0 + -7

Combine like terms: 0 + -7 = -7
-4n = -7

Divide each side by '-4'.
n = 1.75

Simplifying
n = 1.75
Solution
n = {-5, 1.75}