n(n-5)+n(n+2)=2n(n-1)+1.5

Solution for n(n-5)+n(n+2)=2n(n-1)+1.5 equation:

Simplifying
n(n + -5) + n(n + 2) = 2n(n + -1) + 1.5

Reorder the terms:
n(-5 + n) + n(n + 2) = 2n(n + -1) + 1.5
(-5 * n + n * n) + n(n + 2) = 2n(n + -1) + 1.5
(-5n + n2) + n(n + 2) = 2n(n + -1) + 1.5

Reorder the terms:
-5n + n2 + n(2 + n) = 2n(n + -1) + 1.5
-5n + n2 + (2 * n + n * n) = 2n(n + -1) + 1.5
-5n + n2 + (2n + n2) = 2n(n + -1) + 1.5

Reorder the terms:
-5n + 2n + n2 + n2 = 2n(n + -1) + 1.5

Combine like terms: -5n + 2n = -3n
-3n + n2 + n2 = 2n(n + -1) + 1.5

Combine like terms: n2 + n2 = 2n2
-3n + 2n2 = 2n(n + -1) + 1.5

Reorder the terms:
-3n + 2n2 = 2n(-1 + n) + 1.5
-3n + 2n2 = (-1 * 2n + n * 2n) + 1.5
-3n + 2n2 = (-2n + 2n2) + 1.5

Reorder the terms:
-3n + 2n2 = 1.5 + -2n + 2n2

Add '-2n2' to each side of the equation.
-3n + 2n2 + -2n2 = 1.5 + -2n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-3n + 0 = 1.5 + -2n + 2n2 + -2n2
-3n = 1.5 + -2n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-3n = 1.5 + -2n + 0
-3n = 1.5 + -2n

Solving
-3n = 1.5 + -2n

Solving for variable 'n'.

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

Add '2n' to each side of the equation.
-3n + 2n = 1.5 + -2n + 2n

Combine like terms: -3n + 2n = -1n
-1n = 1.5 + -2n + 2n

Combine like terms: -2n + 2n = 0
-1n = 1.5 + 0
-1n = 1.5

Divide each side by '-1'.
n = -1.5

Simplifying
n = -1.5