3(n-5)n-5=21

Simple and best practice solution for 3(n-5)n-5=21 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 3(n-5)n-5=21 equation: 


Simplifying
3(n + -5) * n + -5 = 21

Reorder the terms:
3(-5 + n) * n + -5 = 21

Reorder the terms for easier multiplication:
3n(-5 + n) + -5 = 21
(-5 * 3n + n * 3n) + -5 = 21
(-15n + 3n2) + -5 = 21

Reorder the terms:
-5 + -15n + 3n2 = 21

Solving
-5 + -15n + 3n2 = 21

Solving for variable 'n'.

Reorder the terms:
-5 + -21 + -15n + 3n2 = 21 + -21

Combine like terms: -5 + -21 = -26
-26 + -15n + 3n2 = 21 + -21

Combine like terms: 21 + -21 = 0
-26 + -15n + 3n2 = 0

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

Divide each side by '3'.
-8.666666667 + -5n + n2 = 0

Move the constant term to the right:

Add '8.666666667' to each side of the equation.
-8.666666667 + -5n + 8.666666667 + n2 = 0 + 8.666666667

Reorder the terms:
-8.666666667 + 8.666666667 + -5n + n2 = 0 + 8.666666667

Combine like terms: -8.666666667 + 8.666666667 = 0.000000000
0.000000000 + -5n + n2 = 0 + 8.666666667
-5n + n2 = 0 + 8.666666667

Combine like terms: 0 + 8.666666667 = 8.666666667
-5n + n2 = 8.666666667

The n term is -5n.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5n + 6.25 + n2 = 8.666666667 + 6.25

Reorder the terms:
6.25 + -5n + n2 = 8.666666667 + 6.25

Combine like terms: 8.666666667 + 6.25 = 14.916666667
6.25 + -5n + n2 = 14.916666667

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 14.916666667

Calculate the square root of the right side: 3.862210075

Break this problem into two subproblems by setting 
(n + -2.5) equal to 3.862210075 and -3.862210075.


Subproblem 1
n + -2.5 = 3.862210075

Simplifying
n + -2.5 = 3.862210075

Reorder the terms:
-2.5 + n = 3.862210075

Solving
-2.5 + n = 3.862210075

Solving for variable 'n'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = 3.862210075 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = 3.862210075 + 2.5
n = 3.862210075 + 2.5

Combine like terms: 3.862210075 + 2.5 = 6.362210075
n = 6.362210075

Simplifying
n = 6.362210075


Subproblem 2
n + -2.5 = -3.862210075

Simplifying
n + -2.5 = -3.862210075

Reorder the terms:
-2.5 + n = -3.862210075

Solving
-2.5 + n = -3.862210075

Solving for variable 'n'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = -3.862210075 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = -3.862210075 + 2.5
n = -3.862210075 + 2.5

Combine like terms: -3.862210075 + 2.5 = -1.362210075
n = -1.362210075

Simplifying
n = -1.362210075


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.362210075, -1.362210075}

See similar equations:

| -21.7-1.5= | | 4(4)+3y=16 | | 4x+3(5x-20)=16 | | 2x+5yz=100 | | 5(x-10)=8(x-7) | | f(x)=x^2+2kx+k | | -2(5+x)=3 | | -2(5+x)=-3 | | 9x^5+6x^3+3x^2= | | 5x+3=-24+2x | | (8-3x)-9=18 | | 7*(-6x-3)=-3*(-3x+3) | | X+30=3y | | 9-3(8b-2a)+7(2b-4a)= | | 2x+30=5y+20 | | (w+6)=2w^2+2w+60 | | y=4x^2+5x-9 | | 13b-19=7(5-2b) | | 2x*x+x-6=0 | | 23B-19=7(5-2b) | | 3v^2-10v-8= | | 2(7F+13)=56 | | Y+1(24+9)-28=21 | | 2(7F+13)=54 | | 5(8a+16)=80 | | 12t-6t= | | 13.50x-540=1500 | | 7x^2+4y^2=28 | | 13.50x-540=4158 | | -71=3y+4y-29 | | .05x+.1(15-x)=1.15 | | 45=v+4v |

Equations solver categories