-4n(n+4)=5(n-14)-3n

Solution for -4n(n+4)=5(n-14)-3n equation:

Simplifying
-4n(n + 4) = 5(n + -14) + -3n

Reorder the terms:
-4n(4 + n) = 5(n + -14) + -3n
(4 * -4n + n * -4n) = 5(n + -14) + -3n
(-16n + -4n2) = 5(n + -14) + -3n

Reorder the terms:
-16n + -4n2 = 5(-14 + n) + -3n
-16n + -4n2 = (-14 * 5 + n * 5) + -3n
-16n + -4n2 = (-70 + 5n) + -3n

Combine like terms: 5n + -3n = 2n
-16n + -4n2 = -70 + 2n

Solving
-16n + -4n2 = -70 + 2n

Solving for variable 'n'.

Reorder the terms:
70 + -16n + -2n + -4n2 = -70 + 2n + 70 + -2n

Combine like terms: -16n + -2n = -18n
70 + -18n + -4n2 = -70 + 2n + 70 + -2n

Reorder the terms:
70 + -18n + -4n2 = -70 + 70 + 2n + -2n

Combine like terms: -70 + 70 = 0
70 + -18n + -4n2 = 0 + 2n + -2n
70 + -18n + -4n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
70 + -18n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -9n + -2n2) = 0

Factor a trinomial.
2((5 + -2n)(7 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 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 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Subproblem 2
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 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 + n = 0 + -7

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

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

Simplifying
n = -7
Solution
n = {2.5, -7}