5y^2+40y-75=0

Simple and best practice solution for 5y^2+40y-75=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 5y^2+40y-75=0 equation: 


Simplifying
5y2 + 40y + -75 = 0

Reorder the terms:
-75 + 40y + 5y2 = 0

Solving
-75 + 40y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + 8y + y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-15 + 8y + y2)' equal to zero and attempt to solve:

Simplifying
-15 + 8y + y2 = 0

Solving
-15 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + 8y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8y + y2 = 0 + 15
8y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
8y + y2 = 15

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 15 + 16

Reorder the terms:
16 + 8y + y2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + 8y + y2 = 31

Factor a perfect square on the left side:
(y + 4)(y + 4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(y + 4) equal to 5.567764363 and -5.567764363.


Subproblem 1
y + 4 = 5.567764363

Simplifying
y + 4 = 5.567764363

Reorder the terms:
4 + y = 5.567764363

Solving
4 + y = 5.567764363

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 5.567764363 + -4

Combine like terms: 4 + -4 = 0
0 + y = 5.567764363 + -4
y = 5.567764363 + -4

Combine like terms: 5.567764363 + -4 = 1.567764363
y = 1.567764363

Simplifying
y = 1.567764363


Subproblem 2
y + 4 = -5.567764363

Simplifying
y + 4 = -5.567764363

Reorder the terms:
4 + y = -5.567764363

Solving
4 + y = -5.567764363

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -5.567764363 + -4

Combine like terms: 4 + -4 = 0
0 + y = -5.567764363 + -4
y = -5.567764363 + -4

Combine like terms: -5.567764363 + -4 = -9.567764363
y = -9.567764363

Simplifying
y = -9.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.567764363, -9.567764363}
Solution
y = {1.567764363, -9.567764363}

See similar equations:

| .28x=2556.36 | | 4+6=446 | | 4n-24=56 | | 5x-55=-130 | | 5n+5-7n=15-12n+10n-10 | | 0.5(4x-8)=6x+10 | | 3G+24=9f | | -8x^2+12x+2=4x | | (x+1)(x+2)(x-2)=x^3+8 | | t*3-4=15 | | 9xy/7= | | -58+5y+4=3(4y-3)-3 | | 7m-22=32 | | 3/(w-3)-3/5=w/(w-3) | | 4x+5x=2 | | y^-2=4/16 | | x^2+2x^2=80 | | 5n+11=21 | | 7x=86 | | 9xy/7 | | 11p+7-3p+15=14p+2-2p | | (4/7)x20 | | 12-2x=8-2/5x | | graphy=-6x | | -8x+8=6x-24 | | 8-4/7x12 | | 5(5z+1)-9=121 | | -15y=-5x+75 | | y+0x=11 | | 2x+7-x=8+3x-5 | | y+-2x=11 | | y+-2=11 |

Equations solver categories