4n-7n(n-9)=42

Simple and best practice solution for 4n-7n(n-9)=42 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 4n-7n(n-9)=42 equation:


Simplifying
4n + -7n(n + -9) = 42

Reorder the terms:
4n + -7n(-9 + n) = 42
4n + (-9 * -7n + n * -7n) = 42
4n + (63n + -7n2) = 42

Combine like terms: 4n + 63n = 67n
67n + -7n2 = 42

Solving
67n + -7n2 = 42

Solving for variable 'n'.

Reorder the terms:
-42 + 67n + -7n2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 67n + -7n2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
6 + -9.571428571n + n2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -9.571428571n + -6 + n2 = 0 + -6

Reorder the terms:
6 + -6 + -9.571428571n + n2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9.571428571n + n2 = 0 + -6
-9.571428571n + n2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9.571428571n + n2 = -6

The n term is -9.571428571n.  Take half its coefficient (-4.785714286).
Square it (22.90306123) and add it to both sides.

Add '22.90306123' to each side of the equation.
-9.571428571n + 22.90306123 + n2 = -6 + 22.90306123

Reorder the terms:
22.90306123 + -9.571428571n + n2 = -6 + 22.90306123

Combine like terms: -6 + 22.90306123 = 16.90306123
22.90306123 + -9.571428571n + n2 = 16.90306123

Factor a perfect square on the left side:
(n + -4.785714286)(n + -4.785714286) = 16.90306123

Calculate the square root of the right side: 4.111333267

Break this problem into two subproblems by setting 
(n + -4.785714286) equal to 4.111333267 and -4.111333267.

Subproblem 1

n + -4.785714286 = 4.111333267 Simplifying n + -4.785714286 = 4.111333267 Reorder the terms: -4.785714286 + n = 4.111333267 Solving -4.785714286 + n = 4.111333267 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.785714286' to each side of the equation. -4.785714286 + 4.785714286 + n = 4.111333267 + 4.785714286 Combine like terms: -4.785714286 + 4.785714286 = 0.000000000 0.000000000 + n = 4.111333267 + 4.785714286 n = 4.111333267 + 4.785714286 Combine like terms: 4.111333267 + 4.785714286 = 8.897047553 n = 8.897047553 Simplifying n = 8.897047553

Subproblem 2

n + -4.785714286 = -4.111333267 Simplifying n + -4.785714286 = -4.111333267 Reorder the terms: -4.785714286 + n = -4.111333267 Solving -4.785714286 + n = -4.111333267 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.785714286' to each side of the equation. -4.785714286 + 4.785714286 + n = -4.111333267 + 4.785714286 Combine like terms: -4.785714286 + 4.785714286 = 0.000000000 0.000000000 + n = -4.111333267 + 4.785714286 n = -4.111333267 + 4.785714286 Combine like terms: -4.111333267 + 4.785714286 = 0.674381019 n = 0.674381019 Simplifying n = 0.674381019

Solution

The solution to the problem is based on the solutions from the subproblems. n = {8.897047553, 0.674381019}

See similar equations:

| (x+4)=-24 | | (2x-5w)(4x-7w)= | | -4x-8+5x=15 | | (5x+30)+(3x-10)= | | -8.2x+434=384.8 | | 5(5)+9(4)-3= | | x/9-6=-8 | | 4n-7(1n-9)=42 | | 38+2x=-5(-7x-1) | | 2(2+2x)-8=4 | | 4x^6-16x+16=0 | | 8.5x+421=446.5 | | 6s+16=130 | | (n-3)=-12 | | 3v+2=8v-6 | | -3a+18=-(-3+8a) | | h/4-3=-5 | | y=1/3x2 | | 7h*4=26 | | 7m-7=21 | | x^4+6x^3+11x^2+6x-120=0 | | 4(1-7n)=-38-7n | | x+15-3(x+2)=11 | | 84=3(7-5x) | | ((5x)^(5/2)x^(-4/5))/sqrt5x^3 | | -11+4v=-6(-2v+5)-5 | | 3[2x+3]-4x=-3 | | 8+7(k-6)=-37+7k | | 4(-v+6)=18-4v | | -55+3x=20-2x | | -21+5a=4(a-7) | | 4m-12=15+5m |

Equations solver categories