3n(n-8)=30

Simple and best practice solution for 3n(n-8)=30 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 3n(n-8)=30 equation: 


Simplifying
3n(n + -8) = 30

Reorder the terms:
3n(-8 + n) = 30
(-8 * 3n + n * 3n) = 30
(-24n + 3n2) = 30

Solving
-24n + 3n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -24n + 3n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -24n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -8n + n2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + -8n + n2)' equal to zero and attempt to solve:

Simplifying
-10 + -8n + n2 = 0

Solving
-10 + -8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -8n + 10 + n2 = 0 + 10

Reorder the terms:
-10 + 10 + -8n + n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -8n + n2 = 0 + 10
-8n + n2 = 0 + 10

Combine like terms: 0 + 10 = 10
-8n + n2 = 10

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = 10 + 16

Reorder the terms:
16 + -8n + n2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + -8n + n2 = 26

Factor a perfect square on the left side:
(n + -4)(n + -4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(n + -4) equal to 5.099019514 and -5.099019514.


Subproblem 1
n + -4 = 5.099019514

Simplifying
n + -4 = 5.099019514

Reorder the terms:
-4 + n = 5.099019514

Solving
-4 + n = 5.099019514

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = 5.099019514 + 4

Combine like terms: -4 + 4 = 0
0 + n = 5.099019514 + 4
n = 5.099019514 + 4

Combine like terms: 5.099019514 + 4 = 9.099019514
n = 9.099019514

Simplifying
n = 9.099019514


Subproblem 2
n + -4 = -5.099019514

Simplifying
n + -4 = -5.099019514

Reorder the terms:
-4 + n = -5.099019514

Solving
-4 + n = -5.099019514

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = -5.099019514 + 4

Combine like terms: -4 + 4 = 0
0 + n = -5.099019514 + 4
n = -5.099019514 + 4

Combine like terms: -5.099019514 + 4 = -1.099019514
n = -1.099019514

Simplifying
n = -1.099019514


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.099019514, -1.099019514}
Solution
n = {9.099019514, -1.099019514}

See similar equations:

| 7-2m=-m-(m-6) | | 15n+5n= | | .75w+36=.6666667w+17 | | 2-y=5/7 | | 6(3+3x)+3x=-x-4 | | 9-5t=-16 | | 30x=40+10x | | 2x/5=8/10 | | x+112+46= | | 3a^2-5a+7=5 | | 3x+18=6y | | 8b+6=-2(-4b+3)+8 | | 14.25=x-19.50 | | -2x+5=-33333333333 | | v^2+5v+8=8 | | 2x+5=12-3x | | 4y^2-5y-4= | | X+0.2X=3762 | | -12(8x+9)+2=(5x+10) | | 7d-3d-2d-8=3d | | (-6.4)(4.5)= | | 2/5=-2/9x | | 6y-x=12 | | -32-7b=-2(b-4) | | X+0.1X=3762 | | 3c+9=21 | | Q=3x+7y | | 8=4[-4x-2] | | 5*z+3=23 | | 5x^3-19=0 | | Q=3x+7 | | 2-x=1/x |

Equations solver categories