6n^2=-10n-2

Simple and best practice solution for 6n^2=-10n-2 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 6n^2=-10n-2 equation:


Simplifying
6n2 = -10n + -2

Reorder the terms:
6n2 = -2 + -10n

Solving
6n2 = -2 + -10n

Solving for variable 'n'.

Reorder the terms:
2 + 10n + 6n2 = -2 + -10n + 2 + 10n

Reorder the terms:
2 + 10n + 6n2 = -2 + 2 + -10n + 10n

Combine like terms: -2 + 2 = 0
2 + 10n + 6n2 = 0 + -10n + 10n
2 + 10n + 6n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
2 + 10n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5n + 3n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 5n + 3n2)' equal to zero and attempt to solve: Simplifying 1 + 5n + 3n2 = 0 Solving 1 + 5n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 1.666666667n + n2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.666666667n + -0.3333333333 + n2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.666666667n + n2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.666666667n + n2 = 0 + -0.3333333333 1.666666667n + n2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.666666667n + n2 = -0.3333333333 The n term is 1.666666667n. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667n + 0.6944444447 + n2 = -0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667n + n2 = -0.3333333333 + 0.6944444447 Combine like terms: -0.3333333333 + 0.6944444447 = 0.3611111114 0.6944444447 + 1.666666667n + n2 = 0.3611111114 Factor a perfect square on the left side: (n + 0.8333333335)(n + 0.8333333335) = 0.3611111114 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (n + 0.8333333335) equal to 0.600925213 and -0.600925213.

Subproblem 1

n + 0.8333333335 = 0.600925213 Simplifying n + 0.8333333335 = 0.600925213 Reorder the terms: 0.8333333335 + n = 0.600925213 Solving 0.8333333335 + n = 0.600925213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + n = 0.600925213 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + n = 0.600925213 + -0.8333333335 n = 0.600925213 + -0.8333333335 Combine like terms: 0.600925213 + -0.8333333335 = -0.2324081205 n = -0.2324081205 Simplifying n = -0.2324081205

Subproblem 2

n + 0.8333333335 = -0.600925213 Simplifying n + 0.8333333335 = -0.600925213 Reorder the terms: 0.8333333335 + n = -0.600925213 Solving 0.8333333335 + n = -0.600925213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + n = -0.600925213 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + n = -0.600925213 + -0.8333333335 n = -0.600925213 + -0.8333333335 Combine like terms: -0.600925213 + -0.8333333335 = -1.4342585465 n = -1.4342585465 Simplifying n = -1.4342585465

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.2324081205, -1.4342585465}

Solution

n = {-0.2324081205, -1.4342585465}

See similar equations:

| sqrt(8u^5x)sqrt(2u^3x^8)= | | (a+6)(a-9)=-6a | | (a+6)(a-9)=-6a | | -3.2x+1.1=-14.9 | | solvez^2+20z-121=0 | | m+6-2m+3m=4m-24+16 | | 0.5625L-1.125=0.375L | | 16x-3y=8 | | -16t^2-5t+500=d | | (7x-6)(x-2)=0 | | 4y^3-2y^2-30y=0 | | -7-5=3x+2-2x | | 4x^3+18x^2+18x=0 | | x-5=-3+4 | | n=-11+25 | | 4x-64x^3=0 | | -11q=-69.3-1.1q | | 5x^2+5x-13=29-24x | | 13x+28=5x+228 | | 5x+5x-13=29-24x | | y=x^3+4x^2+4x | | 6p^2-p-2=0 | | 9y^2-24y+15=0 | | 8y-5=13y+40 | | 6-8x=57-29x | | 50-30-15-6=51 | | 1*1=a | | -8(9+y)=-40 | | 3w(l)=13500 | | 4w^6+9m^2=0 | | 6(x+1.38)=5x | | 5=abc |

Equations solver categories