n(n-1.2)=30

Solution for n(n-1.2)=30 equation:

Simplifying
n(n + -1.2) = 30

Reorder the terms:
n(-1.2 + n) = 30
(-1.2 * n + n * n) = 30
(-1.2n + n2) = 30

Solving
-1.2n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -1.2n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -1.2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -1.2n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + -1.2n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1.2n + n2 = 0 + 30
-1.2n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
-1.2n + n2 = 30

The n term is -1.2n.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2n + 0.36 + n2 = 30 + 0.36

Reorder the terms:
0.36 + -1.2n + n2 = 30 + 0.36

Combine like terms: 30 + 0.36 = 30.36
0.36 + -1.2n + n2 = 30.36

Factor a perfect square on the left side:
(n + -0.6)(n + -0.6) = 30.36

Calculate the square root of the right side: 5.509990926

Break this problem into two subproblems by setting 
(n + -0.6) equal to 5.509990926 and -5.509990926.

Subproblem 1
n + -0.6 = 5.509990926

Simplifying
n + -0.6 = 5.509990926

Reorder the terms:
-0.6 + n = 5.509990926

Solving
-0.6 + n = 5.509990926

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = 5.509990926 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = 5.509990926 + 0.6
n = 5.509990926 + 0.6

Combine like terms: 5.509990926 + 0.6 = 6.109990926
n = 6.109990926

Simplifying
n = 6.109990926

Subproblem 2
n + -0.6 = -5.509990926

Simplifying
n + -0.6 = -5.509990926

Reorder the terms:
-0.6 + n = -5.509990926

Solving
-0.6 + n = -5.509990926

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = -5.509990926 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = -5.509990926 + 0.6
n = -5.509990926 + 0.6

Combine like terms: -5.509990926 + 0.6 = -4.909990926
n = -4.909990926

Simplifying
n = -4.909990926

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.109990926, -4.909990926}