12n^2+8n-7920=0

Simple and best practice solution for 12n^2+8n-7920=0 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 12n^2+8n-7920=0 equation: 


Simplifying
12n2 + 8n + -7920 = 0

Reorder the terms:
-7920 + 8n + 12n2 = 0

Solving
-7920 + 8n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1980 + 2n + 3n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1980 + 2n + 3n2)' equal to zero and attempt to solve:

Simplifying
-1980 + 2n + 3n2 = 0

Solving
-1980 + 2n + 3n2 = 0

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

Divide each side by '3'.
-660 + 0.6666666667n + n2 = 0

Move the constant term to the right:

Add '660' to each side of the equation.
-660 + 0.6666666667n + 660 + n2 = 0 + 660

Reorder the terms:
-660 + 660 + 0.6666666667n + n2 = 0 + 660

Combine like terms: -660 + 660 = 0
0 + 0.6666666667n + n2 = 0 + 660
0.6666666667n + n2 = 0 + 660

Combine like terms: 0 + 660 = 660
0.6666666667n + n2 = 660

The n term is 0.6666666667n.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667n + 0.1111111112 + n2 = 660 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667n + n2 = 660 + 0.1111111112

Combine like terms: 660 + 0.1111111112 = 660.1111111112
0.1111111112 + 0.6666666667n + n2 = 660.1111111112

Factor a perfect square on the left side:
(n + 0.3333333334)(n + 0.3333333334) = 660.1111111112

Calculate the square root of the right side: 25.692627563

Break this problem into two subproblems by setting 
(n + 0.3333333334) equal to 25.692627563 and -25.692627563.


Subproblem 1
n + 0.3333333334 = 25.692627563

Simplifying
n + 0.3333333334 = 25.692627563

Reorder the terms:
0.3333333334 + n = 25.692627563

Solving
0.3333333334 + n = 25.692627563

Solving for variable 'n'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + n = 25.692627563 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + n = 25.692627563 + -0.3333333334
n = 25.692627563 + -0.3333333334

Combine like terms: 25.692627563 + -0.3333333334 = 25.3592942296
n = 25.3592942296

Simplifying
n = 25.3592942296


Subproblem 2
n + 0.3333333334 = -25.692627563

Simplifying
n + 0.3333333334 = -25.692627563

Reorder the terms:
0.3333333334 + n = -25.692627563

Solving
0.3333333334 + n = -25.692627563

Solving for variable 'n'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + n = -25.692627563 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + n = -25.692627563 + -0.3333333334
n = -25.692627563 + -0.3333333334

Combine like terms: -25.692627563 + -0.3333333334 = -26.0259608964
n = -26.0259608964

Simplifying
n = -26.0259608964


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {25.3592942296, -26.0259608964}
Solution
n = {25.3592942296, -26.0259608964}

See similar equations:

| 25.6-1.4y+y=24 | | -3r+-15=-35 | | 2(-7x+6)= | | 18-5(4.7-1.7)= | | -3m+6n=5m | | -4y+6=23y-7 | | x+6+2x-1.5=4x-3 | | A-13=-15 | | -7x-10x-60=-196 | | 2z-4+-z=4 | | Y-19=-9 | | 3*3-4(9-4)=x | | 5(x-7)=2 | | 0.6(x-4)=0.5(2x-6) | | 2x+(4-3x)=7 | | 6x-2x+8x=x+5 | | 2y+3x=4x-7y | | 15p+9=5p+5 | | -3(r+5)=-31 | | 3-10a-8=-37 | | 169x^2-78x+c=0 | | mp+mq=t | | -12a+4-10a= | | B-2+8b=32 | | 10-4h=h | | 10x+14y=256 | | (6a)(a-5)= | | 3px=2q(r-5x)forx | | 70=-7(-2-20) | | -6x-6=1-7x | | 2-x=-8 | | 25x^2-148x-12=0 |

Equations solver categories