3n^2+21n-288=0

Simple and best practice solution for 3n^2+21n-288=0 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 3n^2+21n-288=0 equation:


Simplifying
3n2 + 21n + -288 = 0

Reorder the terms:
-288 + 21n + 3n2 = 0

Solving
-288 + 21n + 3n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-96 + 7n + n2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-96 + 7n + n2)' equal to zero and attempt to solve: Simplifying -96 + 7n + n2 = 0 Solving -96 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 7n + 96 + n2 = 0 + 96 Reorder the terms: -96 + 96 + 7n + n2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 7n + n2 = 0 + 96 7n + n2 = 0 + 96 Combine like terms: 0 + 96 = 96 7n + n2 = 96 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 96 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 96 + 12.25 Combine like terms: 96 + 12.25 = 108.25 12.25 + 7n + n2 = 108.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (n + 3.5) equal to 10.404326023 and -10.404326023.

Subproblem 1

n + 3.5 = 10.404326023 Simplifying n + 3.5 = 10.404326023 Reorder the terms: 3.5 + n = 10.404326023 Solving 3.5 + n = 10.404326023 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 10.404326023 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 10.404326023 + -3.5 n = 10.404326023 + -3.5 Combine like terms: 10.404326023 + -3.5 = 6.904326023 n = 6.904326023 Simplifying n = 6.904326023

Subproblem 2

n + 3.5 = -10.404326023 Simplifying n + 3.5 = -10.404326023 Reorder the terms: 3.5 + n = -10.404326023 Solving 3.5 + n = -10.404326023 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -10.404326023 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -10.404326023 + -3.5 n = -10.404326023 + -3.5 Combine like terms: -10.404326023 + -3.5 = -13.904326023 n = -13.904326023 Simplifying n = -13.904326023

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.904326023, -13.904326023}

Solution

n = {6.904326023, -13.904326023}

See similar equations:

| 2(5n+5)= | | 3sqrt8x^6/x^3 | | 20*log(x)=0 | | -0.888x+0.666=0.555 | | .5x+2y=1 | | -6x-13x=-114 | | 4(3x+1)+2x=-12 | | 4x+453=4669 | | n(2x-1)=8 | | 4x+453=3443233 | | 15n+20=125 | | -3(v+1)=8v-14 | | 2(3x+6)=2x-3 | | -3p-7(p+1)=-27 | | 2x+10x^2=0 | | log(3x)=log(4)+log(x-5) | | 4+3x=2(x-4) | | 27-7y=27 | | 16-3x=-6x+4 | | 10/8=4/m-1 | | 5/2=4/b | | 4x+453=34432333 | | 10/7=m/10 | | (x^2+2x-8)(x-6)=0 | | 6/7=5/N | | 4x+453=344323 | | 5(m-6)=6 | | 3+(x+4)+6x=8 | | 4(6x-26)=33 | | c-3=36+3 | | n/6=8/2 | | dy/dx=e^(7x) |

Equations solver categories