8n*2-2(2n-7)(2n+6)=11n

Simple and best practice solution for 8n*2-2(2n-7)(2n+6)=11n 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 8n*2-2(2n-7)(2n+6)=11n equation:


Simplifying
8n * 2 + -2(2n + -7)(2n + 6) = 11n

Reorder the terms for easier multiplication:
8 * 2n + -2(2n + -7)(2n + 6) = 11n

Multiply 8 * 2
16n + -2(2n + -7)(2n + 6) = 11n

Reorder the terms:
16n + -2(-7 + 2n)(2n + 6) = 11n

Reorder the terms:
16n + -2(-7 + 2n)(6 + 2n) = 11n

Multiply (-7 + 2n) * (6 + 2n)
16n + -2(-7(6 + 2n) + 2n * (6 + 2n)) = 11n
16n + -2((6 * -7 + 2n * -7) + 2n * (6 + 2n)) = 11n
16n + -2((-42 + -14n) + 2n * (6 + 2n)) = 11n
16n + -2(-42 + -14n + (6 * 2n + 2n * 2n)) = 11n
16n + -2(-42 + -14n + (12n + 4n2)) = 11n

Combine like terms: -14n + 12n = -2n
16n + -2(-42 + -2n + 4n2) = 11n
16n + (-42 * -2 + -2n * -2 + 4n2 * -2) = 11n
16n + (84 + 4n + -8n2) = 11n

Reorder the terms:
84 + 16n + 4n + -8n2 = 11n

Combine like terms: 16n + 4n = 20n
84 + 20n + -8n2 = 11n

Solving
84 + 20n + -8n2 = 11n

Solving for variable 'n'.

Reorder the terms:
84 + 20n + -11n + -8n2 = 11n + -11n

Combine like terms: 20n + -11n = 9n
84 + 9n + -8n2 = 11n + -11n

Combine like terms: 11n + -11n = 0
84 + 9n + -8n2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-10.5 + -1.125n + n2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -1.125n + 10.5 + n2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -1.125n + n2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -1.125n + n2 = 0 + 10.5
-1.125n + n2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-1.125n + n2 = 10.5

The n term is -1.125n.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125n + 0.31640625 + n2 = 10.5 + 0.31640625

Reorder the terms:
0.31640625 + -1.125n + n2 = 10.5 + 0.31640625

Combine like terms: 10.5 + 0.31640625 = 10.81640625
0.31640625 + -1.125n + n2 = 10.81640625

Factor a perfect square on the left side:
(n + -0.5625)(n + -0.5625) = 10.81640625

Calculate the square root of the right side: 3.288830529

Break this problem into two subproblems by setting 
(n + -0.5625) equal to 3.288830529 and -3.288830529.

Subproblem 1

n + -0.5625 = 3.288830529 Simplifying n + -0.5625 = 3.288830529 Reorder the terms: -0.5625 + n = 3.288830529 Solving -0.5625 + n = 3.288830529 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + n = 3.288830529 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + n = 3.288830529 + 0.5625 n = 3.288830529 + 0.5625 Combine like terms: 3.288830529 + 0.5625 = 3.851330529 n = 3.851330529 Simplifying n = 3.851330529

Subproblem 2

n + -0.5625 = -3.288830529 Simplifying n + -0.5625 = -3.288830529 Reorder the terms: -0.5625 + n = -3.288830529 Solving -0.5625 + n = -3.288830529 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + n = -3.288830529 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + n = -3.288830529 + 0.5625 n = -3.288830529 + 0.5625 Combine like terms: -3.288830529 + 0.5625 = -2.726330529 n = -2.726330529 Simplifying n = -2.726330529

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.851330529, -2.726330529}

See similar equations:

| 9x+-6y=18 | | 400-36n^2=0 | | 2X^3+X^2-20X+21=0 | | (10y+10)+5x+4x=180 | | y=10x+400 | | -45m+68=84m+-61 | | x(x+1)(x+2)(x+3)(x+4)(x+5)(x+6)(x+7)(x+8)(x+9)(x+10)=0 | | 2x-22=2 | | (1+z)(4z+5)=0 | | 1=5x^5-2x^2 | | -6a+8(-a-2)=-128 | | 9=3y+5x | | x^2+y^2-4x-14=0 | | 2(M-24)+3(M-3)=38 | | x^2+4x+3=(x+3)(x+1)x | | 7x-2=10x-3x | | 12-y=-87-2 | | n-12=-75 | | 31.82-2y=4.5y+3.92 | | x^2+4x+3=(x+3)(x+1) | | n+9=-30 | | 2(x+6)=36-4x | | 2x-26=32 | | 4*y^2+6*x+4*y=35 | | r(x)=x^3+13x^2+48x+36 | | 3y+6(y-2)=24 | | 4+6(2x+7)=118 | | x^2+2x+3=(x+3)(x+1) | | -3(p-3)=2p+4 | | 5x-7=7x-28 | | 1.6-y=12.8+3y | | 10.3+1.05x=-4.1x |

Equations solver categories