8n(3n+7)=3

Simple and best practice solution for 8n(3n+7)=3 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(3n+7)=3 equation:


Simplifying
8n(3n + 7) = 3

Reorder the terms:
8n(7 + 3n) = 3
(7 * 8n + 3n * 8n) = 3
(56n + 24n2) = 3

Solving
56n + 24n2 = 3

Solving for variable 'n'.

Reorder the terms:
-3 + 56n + 24n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 56n + 24n2 = 0

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

Divide each side by '24'.
-0.125 + 2.333333333n + n2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 2.333333333n + 0.125 + n2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 2.333333333n + n2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 2.333333333n + n2 = 0 + 0.125
2.333333333n + n2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
2.333333333n + n2 = 0.125

The n term is 2.333333333n.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333n + 1.361111112 + n2 = 0.125 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333n + n2 = 0.125 + 1.361111112

Combine like terms: 0.125 + 1.361111112 = 1.486111112
1.361111112 + 2.333333333n + n2 = 1.486111112

Factor a perfect square on the left side:
(n + 1.166666667)(n + 1.166666667) = 1.486111112

Calculate the square root of the right side: 1.21906157

Break this problem into two subproblems by setting 
(n + 1.166666667) equal to 1.21906157 and -1.21906157.

Subproblem 1

n + 1.166666667 = 1.21906157 Simplifying n + 1.166666667 = 1.21906157 Reorder the terms: 1.166666667 + n = 1.21906157 Solving 1.166666667 + n = 1.21906157 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + n = 1.21906157 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + n = 1.21906157 + -1.166666667 n = 1.21906157 + -1.166666667 Combine like terms: 1.21906157 + -1.166666667 = 0.052394903 n = 0.052394903 Simplifying n = 0.052394903

Subproblem 2

n + 1.166666667 = -1.21906157 Simplifying n + 1.166666667 = -1.21906157 Reorder the terms: 1.166666667 + n = -1.21906157 Solving 1.166666667 + n = -1.21906157 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + n = -1.21906157 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + n = -1.21906157 + -1.166666667 n = -1.21906157 + -1.166666667 Combine like terms: -1.21906157 + -1.166666667 = -2.385728237 n = -2.385728237 Simplifying n = -2.385728237

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.052394903, -2.385728237}

See similar equations:

| 4v-3=3v | | |x-4|+1=8 | | -10x-3=97 | | 4z-2(z+6)=7x+8 | | 6=-3(5n+3) | | 10x-3=20x+97 | | 8m+5n-2m+4n= | | 2(4x+5)-5=8x+5 | | 7=-6x+43 | | 1.56g-10=0.14 | | -5sec^2(x)-4=0 | | 7x+11=3x+43 | | 4(2x+7)=-45+33 | | -9y-10=2y+12 | | 2(x+3)=-3x+26 | | 3x-10=-16 | | sec^2(x)+4=0 | | 2a+3a+a= | | 2x-9y=6 | | |2x+3|+8=3 | | 2x-10=-x-16 | | -2=v+6 | | 8n-7=5+32 | | 2x+3=-6x | | -5x+18=33 | | (x)=7 | | |4x-3|-5=4 | | (x)7= | | 4x+4-10x=3x+5 | | -12=12(v-5) | | -8x+18=-3x+33 | | 4u^2-28u=0 |

Equations solver categories