10n^2=8-12n

Simple and best practice solution for 10n^2=8-12n 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 10n^2=8-12n equation:


Simplifying
10n2 = 8 + -12n

Solving
10n2 = 8 + -12n

Solving for variable 'n'.

Reorder the terms:
-8 + 12n + 10n2 = 8 + -12n + -8 + 12n

Reorder the terms:
-8 + 12n + 10n2 = 8 + -8 + -12n + 12n

Combine like terms: 8 + -8 = 0
-8 + 12n + 10n2 = 0 + -12n + 12n
-8 + 12n + 10n2 = -12n + 12n

Combine like terms: -12n + 12n = 0
-8 + 12n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 6n + 5n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + 6n + 5n2)' equal to zero and attempt to solve: Simplifying -4 + 6n + 5n2 = 0 Solving -4 + 6n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 1.2n + n2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.2n + 0.8 + n2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.2n + n2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.2n + n2 = 0 + 0.8 1.2n + n2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 1.2n + n2 = 0.8 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 = 0.8 + 0.36 Reorder the terms: 0.36 + 1.2n + n2 = 0.8 + 0.36 Combine like terms: 0.8 + 0.36 = 1.16 0.36 + 1.2n + n2 = 1.16 Factor a perfect square on the left side: (n + 0.6)(n + 0.6) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (n + 0.6) equal to 1.077032961 and -1.077032961.

Subproblem 1

n + 0.6 = 1.077032961 Simplifying n + 0.6 = 1.077032961 Reorder the terms: 0.6 + n = 1.077032961 Solving 0.6 + n = 1.077032961 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 = 1.077032961 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = 1.077032961 + -0.6 n = 1.077032961 + -0.6 Combine like terms: 1.077032961 + -0.6 = 0.477032961 n = 0.477032961 Simplifying n = 0.477032961

Subproblem 2

n + 0.6 = -1.077032961 Simplifying n + 0.6 = -1.077032961 Reorder the terms: 0.6 + n = -1.077032961 Solving 0.6 + n = -1.077032961 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 = -1.077032961 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = -1.077032961 + -0.6 n = -1.077032961 + -0.6 Combine like terms: -1.077032961 + -0.6 = -1.677032961 n = -1.677032961 Simplifying n = -1.677032961

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.477032961, -1.677032961}

Solution

n = {0.477032961, -1.677032961}

See similar equations:

| 3+2=13 | | 450x=-50 | | 0.25*x^2-x+0.25=0 | | 8x-1=5x-4 | | h=1/4j(c-d) | | x^3+7x-1=0 | | -9x-24=-3(x+8)-6x | | 17x-216=54+2x | | 16x+6y=63 | | 2n-5=7n+4 | | 10x-5+2x=5x+1+x | | 8=4-2*(3x-8) | | y=0.10x+4 | | x+41=55 | | 2x^3+8x^2=-6x | | 4(c-2)=32 | | ln*2+ln*(x+11)=ln*(4x-8) | | 11x-22=23+10x | | 2x-10y+1=z | | 60=-2(x+3)+x | | 3.3x=2.8x+4.0 | | 450x+50= | | -9x=-8x-24 | | -20u^2-60u-45=0 | | 200m-75+58200=60300-175m | | -5/16=-45 | | 4(x+7)=8x-4(x-5) | | x+3-4x=3 | | 15-3x=-7x+15 | | 2/4=8/n-6 | | 3x+4-x=2 | | 4(x-5)=-17+x |

Equations solver categories