2=-15n(-3n+2)

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Solution for 2=-15n(-3n+2) equation:


Simplifying
2 = -15n(-3n + 2)

Reorder the terms:
2 = -15n(2 + -3n)
2 = (2 * -15n + -3n * -15n)
2 = (-30n + 45n2)

Solving
2 = -30n + 45n2

Solving for variable 'n'.

Reorder the terms:
2 + 30n + -45n2 = -30n + 30n + 45n2 + -45n2

Combine like terms: -30n + 30n = 0
2 + 30n + -45n2 = 0 + 45n2 + -45n2
2 + 30n + -45n2 = 45n2 + -45n2

Combine like terms: 45n2 + -45n2 = 0
2 + 30n + -45n2 = 0

Begin completing the square.  Divide all terms by
-45 the coefficient of the squared term: 

Divide each side by '-45'.
-0.04444444444 + -0.6666666667n + n2 = 0

Move the constant term to the right:

Add '0.04444444444' to each side of the equation.
-0.04444444444 + -0.6666666667n + 0.04444444444 + n2 = 0 + 0.04444444444

Reorder the terms:
-0.04444444444 + 0.04444444444 + -0.6666666667n + n2 = 0 + 0.04444444444

Combine like terms: -0.04444444444 + 0.04444444444 = 0.00000000000
0.00000000000 + -0.6666666667n + n2 = 0 + 0.04444444444
-0.6666666667n + n2 = 0 + 0.04444444444

Combine like terms: 0 + 0.04444444444 = 0.04444444444
-0.6666666667n + n2 = 0.04444444444

The n term is -0.6666666667n.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667n + 0.1111111112 + n2 = 0.04444444444 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667n + n2 = 0.04444444444 + 0.1111111112

Combine like terms: 0.04444444444 + 0.1111111112 = 0.15555555564
0.1111111112 + -0.6666666667n + n2 = 0.15555555564

Factor a perfect square on the left side:
(n + -0.3333333334)(n + -0.3333333334) = 0.15555555564

Calculate the square root of the right side: 0.394405319

Break this problem into two subproblems by setting 
(n + -0.3333333334) equal to 0.394405319 and -0.394405319.

Subproblem 1

n + -0.3333333334 = 0.394405319 Simplifying n + -0.3333333334 = 0.394405319 Reorder the terms: -0.3333333334 + n = 0.394405319 Solving -0.3333333334 + n = 0.394405319 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + n = 0.394405319 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + n = 0.394405319 + 0.3333333334 n = 0.394405319 + 0.3333333334 Combine like terms: 0.394405319 + 0.3333333334 = 0.7277386524 n = 0.7277386524 Simplifying n = 0.7277386524

Subproblem 2

n + -0.3333333334 = -0.394405319 Simplifying n + -0.3333333334 = -0.394405319 Reorder the terms: -0.3333333334 + n = -0.394405319 Solving -0.3333333334 + n = -0.394405319 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + n = -0.394405319 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + n = -0.394405319 + 0.3333333334 n = -0.394405319 + 0.3333333334 Combine like terms: -0.394405319 + 0.3333333334 = -0.0610719856 n = -0.0610719856 Simplifying n = -0.0610719856

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.7277386524, -0.0610719856}

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