0.5*(n+3)*(n-3)=20

Solution for 0.5*(n+3)*(n-3)=20 equation:

Simplifying
0.5(n + 3)(n + -3) = 20

Reorder the terms:
0.5(3 + n)(n + -3) = 20

Reorder the terms:
0.5(3 + n)(-3 + n) = 20

Multiply (3 + n) * (-3 + n)
0.5(3(-3 + n) + n(-3 + n)) = 20
0.5((-3 * 3 + n * 3) + n(-3 + n)) = 20
0.5((-9 + 3n) + n(-3 + n)) = 20
0.5(-9 + 3n + (-3 * n + n * n)) = 20
0.5(-9 + 3n + (-3n + n2)) = 20

Combine like terms: 3n + -3n = 0
0.5(-9 + 0 + n2) = 20
0.5(-9 + n2) = 20
(-9 * 0.5 + n2 * 0.5) = 20
(-4.5 + 0.5n2) = 20

Solving
-4.5 + 0.5n2 = 20

Solving for variable 'n'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + 0.5n2 = 20 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 0.5n2 = 20 + 4.5
0.5n2 = 20 + 4.5

Combine like terms: 20 + 4.5 = 24.5
0.5n2 = 24.5

Divide each side by '0.5'.
n2 = 49

Simplifying
n2 = 49

Take the square root of each side:
n = {-7, 7}