6y^2-28y-480=0

Simple and best practice solution for 6y^2-28y-480=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 6y^2-28y-480=0 equation: 


Simplifying
6y2 + -28y + -480 = 0

Reorder the terms:
-480 + -28y + 6y2 = 0

Solving
-480 + -28y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-240 + -14y + 3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-240 + -14y + 3y2)' equal to zero and attempt to solve:

Simplifying
-240 + -14y + 3y2 = 0

Solving
-240 + -14y + 3y2 = 0

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

Divide each side by '3'.
-80 + -4.666666667y + y2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -4.666666667y + 80 + y2 = 0 + 80

Reorder the terms:
-80 + 80 + -4.666666667y + y2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -4.666666667y + y2 = 0 + 80
-4.666666667y + y2 = 0 + 80

Combine like terms: 0 + 80 = 80
-4.666666667y + y2 = 80

The y term is -4.666666667y.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667y + 5.444444448 + y2 = 80 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667y + y2 = 80 + 5.444444448

Combine like terms: 80 + 5.444444448 = 85.444444448
5.444444448 + -4.666666667y + y2 = 85.444444448

Factor a perfect square on the left side:
(y + -2.333333334)(y + -2.333333334) = 85.444444448

Calculate the square root of the right side: 9.243616416

Break this problem into two subproblems by setting 
(y + -2.333333334) equal to 9.243616416 and -9.243616416.


Subproblem 1
y + -2.333333334 = 9.243616416

Simplifying
y + -2.333333334 = 9.243616416

Reorder the terms:
-2.333333334 + y = 9.243616416

Solving
-2.333333334 + y = 9.243616416

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + y = 9.243616416 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + y = 9.243616416 + 2.333333334
y = 9.243616416 + 2.333333334

Combine like terms: 9.243616416 + 2.333333334 = 11.57694975
y = 11.57694975

Simplifying
y = 11.57694975


Subproblem 2
y + -2.333333334 = -9.243616416

Simplifying
y + -2.333333334 = -9.243616416

Reorder the terms:
-2.333333334 + y = -9.243616416

Solving
-2.333333334 + y = -9.243616416

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + y = -9.243616416 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + y = -9.243616416 + 2.333333334
y = -9.243616416 + 2.333333334

Combine like terms: -9.243616416 + 2.333333334 = -6.910283082
y = -6.910283082

Simplifying
y = -6.910283082


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.57694975, -6.910283082}
Solution
y = {11.57694975, -6.910283082}

See similar equations:

| 35-5x=14-8x | | 3(4x-5)+2x-8=61 | | 3x^2+6x-13=0 | | -4w+6=-2w+16 | | f(2010)=0.72(2010)+2 | | 1x^2+1x-72=0 | | 11c+3=4c+45 | | x*34-23= | | 18=y/4 | | 5x-96=4y | | 5x-96=45 | | Log(3)x=log(9)6x | | -21=2(x-8)+3Y | | (-12x^5y^6/6x^11y^-2) | | (x/6)-(x/7)=5/7 | | (x/4)-(x/5)=9/4 | | -10(78)+0.95x=0.05(x-12) | | -x^2-ix+2=0 | | -17=4x+7 | | (7-6t)/(5t-11) | | 3(v-3)=4(v+1) | | -x-ix+2=0 | | 33=-7x-30 | | x^2-12ix+3i=0 | | 7x-33=86 | | 7x-33=89 | | -16=29-5x | | 52=10+3x | | (4x)+(2x+12)=90 | | 6x+37=-23 | | -24+6r=-102 | | -3p-2(4-6p)=4(p-3)-6 |

Equations solver categories