2n(n-5)=30

Simple and best practice solution for 2n(n-5)=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 2n(n-5)=30 equation: 


Simplifying
2n(n + -5) = 30

Reorder the terms:
2n(-5 + n) = 30
(-5 * 2n + n * 2n) = 30
(-10n + 2n2) = 30

Solving
-10n + 2n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -10n + 2n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -10n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -5n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -5n + n2)' equal to zero and attempt to solve:

Simplifying
-15 + -5n + n2 = 0

Solving
-15 + -5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -5n + 15 + n2 = 0 + 15

Reorder the terms:
-15 + 15 + -5n + n2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -5n + n2 = 0 + 15
-5n + n2 = 0 + 15

Combine like terms: 0 + 15 = 15
-5n + n2 = 15

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 = 15 + 6.25

Reorder the terms:
6.25 + -5n + n2 = 15 + 6.25

Combine like terms: 15 + 6.25 = 21.25
6.25 + -5n + n2 = 21.25

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(n + -2.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
n + -2.5 = 4.609772229

Simplifying
n + -2.5 = 4.609772229

Reorder the terms:
-2.5 + n = 4.609772229

Solving
-2.5 + n = 4.609772229

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 = 4.609772229 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = 4.609772229 + 2.5
n = 4.609772229 + 2.5

Combine like terms: 4.609772229 + 2.5 = 7.109772229
n = 7.109772229

Simplifying
n = 7.109772229


Subproblem 2
n + -2.5 = -4.609772229

Simplifying
n + -2.5 = -4.609772229

Reorder the terms:
-2.5 + n = -4.609772229

Solving
-2.5 + n = -4.609772229

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 = -4.609772229 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = -4.609772229 + 2.5
n = -4.609772229 + 2.5

Combine like terms: -4.609772229 + 2.5 = -2.109772229
n = -2.109772229

Simplifying
n = -2.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.109772229, -2.109772229}
Solution
n = {7.109772229, -2.109772229}

See similar equations:

| 10+x-3*10=8+x+3*8 | | 32/5 | | 7x=2x+75 | | (x+3)64=(x-3)100 | | p-3=30-11 | | (x+3)+8*8=(x-3)+10*10 | | =x^3-4x^2+4x | | 4d+c=d-15 | | x=20+1.33x | | 3-(x+4)=3x-9 | | 7a-4+2a=3a+2 | | 26x-14=-18x+5 | | 15(x)=10(x+1) | | 5(3x-1/5-7)=70 | | 6(1g+3)=-2(1g+31) | | cotx=tanx | | 2(x-3)=2x-2 | | y=9-(100/(100-x)*9) | | 40x^2-16x-4= | | sinx-sqrt(2)=-sinx | | x^2-1.5x=0 | | 9-(((100-x)/100)*9) | | -2(4y-3)+2y=3(y+6) | | -6-3=0 | | 4x*4x-4= | | e^x^2=e^9x·1/e^14 | | 4x*10x= | | a+b+c+d+e=db | | 64b-1/8+45= | | 3.625= | | 4x=9-16y^2 | | y=x+2x^3 |

Equations solver categories