0.5(n+3)(n-3)=56

Solution for 0.5(n+3)(n-3)=56 equation:

Simplifying
0.5(n + 3)(n + -3) = 56

Reorder the terms:
0.5(3 + n)(n + -3) = 56

Reorder the terms:
0.5(3 + n)(-3 + n) = 56

Multiply (3 + n) * (-3 + n)
0.5(3(-3 + n) + n(-3 + n)) = 56
0.5((-3 * 3 + n * 3) + n(-3 + n)) = 56
0.5((-9 + 3n) + n(-3 + n)) = 56
0.5(-9 + 3n + (-3 * n + n * n)) = 56
0.5(-9 + 3n + (-3n + n2)) = 56

Combine like terms: 3n + -3n = 0
0.5(-9 + 0 + n2) = 56
0.5(-9 + n2) = 56
(-9 * 0.5 + n2 * 0.5) = 56
(-4.5 + 0.5n2) = 56

Solving
-4.5 + 0.5n2 = 56

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 = 56 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 0.5n2 = 56 + 4.5
0.5n2 = 56 + 4.5

Combine like terms: 56 + 4.5 = 60.5
0.5n2 = 60.5

Divide each side by '0.5'.
n2 = 121

Simplifying
n2 = 121

Take the square root of each side:
n = {-11, 11}