5(n-2)(n+2)=0

Solution for 5(n-2)(n+2)=0 equation:

Simplifying
5(n + -2)(n + 2) = 0

Reorder the terms:
5(-2 + n)(n + 2) = 0

Reorder the terms:
5(-2 + n)(2 + n) = 0

Multiply (-2 + n) * (2 + n)
5(-2(2 + n) + n(2 + n)) = 0
5((2 * -2 + n * -2) + n(2 + n)) = 0
5((-4 + -2n) + n(2 + n)) = 0
5(-4 + -2n + (2 * n + n * n)) = 0
5(-4 + -2n + (2n + n2)) = 0

Combine like terms: -2n + 2n = 0
5(-4 + 0 + n2) = 0
5(-4 + n2) = 0
(-4 * 5 + n2 * 5) = 0
(-20 + 5n2) = 0

Solving
-20 + 5n2 = 0

Solving for variable 'n'.

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

Add '20' to each side of the equation.
-20 + 20 + 5n2 = 0 + 20

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

Combine like terms: 0 + 20 = 20
5n2 = 20

Divide each side by '5'.
n2 = 4

Simplifying
n2 = 4

Take the square root of each side:
n = {-2, 2}