5n(n+4)=20n+45

Solution for 5n(n+4)=20n+45 equation:

Simplifying
5n(n + 4) = 20n + 45

Reorder the terms:
5n(4 + n) = 20n + 45
(4 * 5n + n * 5n) = 20n + 45
(20n + 5n2) = 20n + 45

Reorder the terms:
20n + 5n2 = 45 + 20n

Add '-20n' to each side of the equation.
20n + -20n + 5n2 = 45 + 20n + -20n

Combine like terms: 20n + -20n = 0
0 + 5n2 = 45 + 20n + -20n
5n2 = 45 + 20n + -20n

Combine like terms: 20n + -20n = 0
5n2 = 45 + 0
5n2 = 45

Solving
5n2 = 45

Solving for variable 'n'.

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

Divide each side by '5'.
n2 = 9

Simplifying
n2 = 9

Take the square root of each side:
n = {-3, 3}