48n-9n^2=36

Simple and best practice solution for 48n-9n^2=36 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 48n-9n^2=36 equation: 


Simplifying
48n + -9n2 = 36

Solving
48n + -9n2 = 36

Solving for variable 'n'.

Reorder the terms:
-36 + 48n + -9n2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 48n + -9n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 16n + -3n2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-12 + 16n + -3n2)' equal to zero and attempt to solve:

Simplifying
-12 + 16n + -3n2 = 0

Solving
-12 + 16n + -3n2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
4 + -5.333333333n + n2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.333333333n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + -5.333333333n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.333333333n + n2 = 0 + -4
-5.333333333n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.333333333n + n2 = -4

The n term is -5.333333333n.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333n + 7.111111113 + n2 = -4 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333n + n2 = -4 + 7.111111113

Combine like terms: -4 + 7.111111113 = 3.111111113
7.111111113 + -5.333333333n + n2 = 3.111111113

Factor a perfect square on the left side:
(n + -2.666666667)(n + -2.666666667) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(n + -2.666666667) equal to 1.763834208 and -1.763834208.


Subproblem 1
n + -2.666666667 = 1.763834208

Simplifying
n + -2.666666667 = 1.763834208

Reorder the terms:
-2.666666667 + n = 1.763834208

Solving
-2.666666667 + n = 1.763834208

Solving for variable 'n'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + n = 1.763834208 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + n = 1.763834208 + 2.666666667
n = 1.763834208 + 2.666666667

Combine like terms: 1.763834208 + 2.666666667 = 4.430500875
n = 4.430500875

Simplifying
n = 4.430500875


Subproblem 2
n + -2.666666667 = -1.763834208

Simplifying
n + -2.666666667 = -1.763834208

Reorder the terms:
-2.666666667 + n = -1.763834208

Solving
-2.666666667 + n = -1.763834208

Solving for variable 'n'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + n = -1.763834208 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + n = -1.763834208 + 2.666666667
n = -1.763834208 + 2.666666667

Combine like terms: -1.763834208 + 2.666666667 = 0.902832459
n = 0.902832459

Simplifying
n = 0.902832459


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.430500875, 0.902832459}
Solution
n = {4.430500875, 0.902832459}

See similar equations:

| -13+y+y^2=0 | | 0=5x^4-2x^2-4 | | -400.00x+4000=0.00 | | -b+ax=cb | | 3a+5(a-4)= | | -4.5=-.5(x-7.1) | | 10x-23=-123 | | (v^2-13v-36)=0 | | -29+s=-58 | | v^2(v^2-13v-36)=0 | | 4-6p+5p= | | ax-b=cb | | 36=24N-3N^2 | | y=-30+5 | | 24N-3N^2=48N-9N^2 | | 22x^2+33x=0 | | 5(x-20)=5(x-4) | | 16+5p=51 | | -400x+4000=2000 | | -(2p-8)-6p=20+4(p+6) | | 3(h-6)=3(h+4) | | w(n)=4n+4 | | 6(2n+5)=54 | | y=12x+480 | | 5x+13=-9x | | (3x+27)(x+25)= | | n^3-5n^2-6n=0 | | 24N-3N^2-36=0 | | T-2z=2m | | 5x+19=-9x | | -4x^2+22x-30=0 | | 0.075-0.5x=x |

Equations solver categories