(n+5)(0.5(n-5))=28

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Solution for (n+5)(0.5(n-5))=28 equation: 


Simplifying
(n + 5)(0.5(n + -5)) = 28

Reorder the terms:
(5 + n)(0.5(n + -5)) = 28

Reorder the terms:
(5 + n)(0.5(-5 + n)) = 28
(5 + n)((-5 * 0.5 + n * 0.5)) = 28
(5 + n)((-2.5 + 0.5n)) = 28

Multiply (5 + n) * (-2.5 + 0.5n)
(5(-2.5 + 0.5n) + n(-2.5 + 0.5n)) = 28
((-2.5 * 5 + 0.5n * 5) + n(-2.5 + 0.5n)) = 28
((-12.5 + 2.5n) + n(-2.5 + 0.5n)) = 28
(-12.5 + 2.5n + (-2.5 * n + 0.5n * n)) = 28
(-12.5 + 2.5n + (-2.5n + 0.5n2)) = 28

Combine like terms: 2.5n + -2.5n = 0.0
(-12.5 + 0.0 + 0.5n2) = 28
(-12.5 + 0.5n2) = 28

Solving
-12.5 + 0.5n2 = 28

Solving for variable 'n'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + 0.5n2 = 28 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 0.5n2 = 28 + 12.5
0.5n2 = 28 + 12.5

Combine like terms: 28 + 12.5 = 40.5
0.5n2 = 40.5

Divide each side by '0.5'.
n2 = 81

Simplifying
n2 = 81

Take the square root of each side:
n = {-9, 9}

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