8n(5n+6)=15

Simple and best practice solution for 8n(5n+6)=15 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(5n+6)=15 equation:


Simplifying
8n(5n + 6) = 15

Reorder the terms:
8n(6 + 5n) = 15
(6 * 8n + 5n * 8n) = 15
(48n + 40n2) = 15

Solving
48n + 40n2 = 15

Solving for variable 'n'.

Reorder the terms:
-15 + 48n + 40n2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 48n + 40n2 = 0

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

Divide each side by '40'.
-0.375 + 1.2n + n2 = 0.0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 1.2n + 0.375 + n2 = 0.0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 1.2n + n2 = 0.0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 1.2n + n2 = 0.0 + 0.375
1.2n + n2 = 0.0 + 0.375

Combine like terms: 0.0 + 0.375 = 0.375
1.2n + n2 = 0.375

The n term is 1.2n.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2n + 0.36 + n2 = 0.375 + 0.36

Reorder the terms:
0.36 + 1.2n + n2 = 0.375 + 0.36

Combine like terms: 0.375 + 0.36 = 0.735
0.36 + 1.2n + n2 = 0.735

Factor a perfect square on the left side:
(n + 0.6)(n + 0.6) = 0.735

Calculate the square root of the right side: 0.85732141

Break this problem into two subproblems by setting 
(n + 0.6) equal to 0.85732141 and -0.85732141.

Subproblem 1

n + 0.6 = 0.85732141 Simplifying n + 0.6 = 0.85732141 Reorder the terms: 0.6 + n = 0.85732141 Solving 0.6 + n = 0.85732141 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + n = 0.85732141 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = 0.85732141 + -0.6 n = 0.85732141 + -0.6 Combine like terms: 0.85732141 + -0.6 = 0.25732141 n = 0.25732141 Simplifying n = 0.25732141

Subproblem 2

n + 0.6 = -0.85732141 Simplifying n + 0.6 = -0.85732141 Reorder the terms: 0.6 + n = -0.85732141 Solving 0.6 + n = -0.85732141 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + n = -0.85732141 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = -0.85732141 + -0.6 n = -0.85732141 + -0.6 Combine like terms: -0.85732141 + -0.6 = -1.45732141 n = -1.45732141 Simplifying n = -1.45732141

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.25732141, -1.45732141}

See similar equations:

| -6+b-8=10-5b | | 9x-y=-6x+y | | 8m-(5n+6)=15 | | 1/9x-10=-30 | | y=(x+1)(6x-6)-6xsqaured | | (t-4)=6 | | -10c=-9c-10 | | 5x+1y=80 | | 9x=x+64 | | -d+15-8d=60 | | 3=3w-3 | | 7s-3=6s+3 | | T+(-10)=0 | | F(x)=x^3-2x^2-2x-3 | | 5y=139 | | 2h-8+10h=52 | | (m+3)2=7 | | 5x-4=23x-2 | | 5(n-13)=30 | | 4+t=-1 | | 3x+8+9x+7+3x=180 | | 12h-8+10h=52 | | 6=12-3u | | 2(m=m2)/8 | | -9x-16=-8x-8 | | -4+7=2y-3 | | -8+8g=6+10g | | 8a-2(5a+7)=20 | | 2q-5s-8q-3s= | | 36/h-g | | 183=8+5(3.50)+5t | | -10=4+m |

Equations solver categories