2n(n-9)=24

Simple and best practice solution for 2n(n-9)=24 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 2n(n-9)=24 equation: 


Simplifying
2n(n + -9) = 24

Reorder the terms:
2n(-9 + n) = 24
(-9 * 2n + n * 2n) = 24
(-18n + 2n2) = 24

Solving
-18n + 2n2 = 24

Solving for variable 'n'.

Reorder the terms:
-24 + -18n + 2n2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -18n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -9n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + -9n + n2)' equal to zero and attempt to solve:

Simplifying
-12 + -9n + n2 = 0

Solving
-12 + -9n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -9n + 12 + n2 = 0 + 12

Reorder the terms:
-12 + 12 + -9n + n2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -9n + n2 = 0 + 12
-9n + n2 = 0 + 12

Combine like terms: 0 + 12 = 12
-9n + n2 = 12

The n term is -9n.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9n + 20.25 + n2 = 12 + 20.25

Reorder the terms:
20.25 + -9n + n2 = 12 + 20.25

Combine like terms: 12 + 20.25 = 32.25
20.25 + -9n + n2 = 32.25

Factor a perfect square on the left side:
(n + -4.5)(n + -4.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(n + -4.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
n + -4.5 = 5.678908346

Simplifying
n + -4.5 = 5.678908346

Reorder the terms:
-4.5 + n = 5.678908346

Solving
-4.5 + n = 5.678908346

Solving for variable 'n'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + n = 5.678908346 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + n = 5.678908346 + 4.5
n = 5.678908346 + 4.5

Combine like terms: 5.678908346 + 4.5 = 10.178908346
n = 10.178908346

Simplifying
n = 10.178908346


Subproblem 2
n + -4.5 = -5.678908346

Simplifying
n + -4.5 = -5.678908346

Reorder the terms:
-4.5 + n = -5.678908346

Solving
-4.5 + n = -5.678908346

Solving for variable 'n'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + n = -5.678908346 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + n = -5.678908346 + 4.5
n = -5.678908346 + 4.5

Combine like terms: -5.678908346 + 4.5 = -1.178908346
n = -1.178908346

Simplifying
n = -1.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.178908346, -1.178908346}
Solution
n = {10.178908346, -1.178908346}

See similar equations:

| 6+4(x-8)=-17-5x | | 4.3x-0.2=8.4 | | 273=68-v | | 8(1-7n)-8=7n | | -10sinx=0 | | -24=3v-6 | | 32-7m=-5(4m+8)-6 | | 75+1.6n=83 | | -6(1-v)=54 | | X+58=2x | | -(1-8v)-2v=-13+2v | | ((3/2)^2)*((2/2)^3) | | 50+7n=I | | -(1+4a)=-1-a | | 3(7k-6)=-5k+34 | | -(6-2p)-3=-p+2(-p-7) | | (x+39)(3x+20)=x | | 5-0.3d=-1 | | y+7-2x=5 | | f(2)=2x | | (4ax/5x^4)(25x/2a) | | 1/16×-8/11-3/4×-8/11=1/2 | | 5(v+4)=-2(7v-4)+9V | | p=34X-132 | | -5x-1-4(3x-3)=4x-8x | | 7.3x=3.3+12 | | 8(-6-p)-6=5p-8(p+8) | | -7-8(m+8)=8m-39 | | 6-4x=1.8 | | 0.5c+0.8=1.3 | | 3n-2-3=-3(-4n-4)-2(n+5) | | 5a-2(a-1)=35-8a |

Equations solver categories