5y(3y-25)=47

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Solution for 5y(3y-25)=47 equation: 


Simplifying
5y(3y + -25) = 47

Reorder the terms:
5y(-25 + 3y) = 47
(-25 * 5y + 3y * 5y) = 47
(-125y + 15y2) = 47

Solving
-125y + 15y2 = 47

Solving for variable 'y'.

Reorder the terms:
-47 + -125y + 15y2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + -125y + 15y2 = 0

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

Divide each side by '15'.
-3.133333333 + -8.333333333y + y2 = 0

Move the constant term to the right:

Add '3.133333333' to each side of the equation.
-3.133333333 + -8.333333333y + 3.133333333 + y2 = 0 + 3.133333333

Reorder the terms:
-3.133333333 + 3.133333333 + -8.333333333y + y2 = 0 + 3.133333333

Combine like terms: -3.133333333 + 3.133333333 = 0.000000000
0.000000000 + -8.333333333y + y2 = 0 + 3.133333333
-8.333333333y + y2 = 0 + 3.133333333

Combine like terms: 0 + 3.133333333 = 3.133333333
-8.333333333y + y2 = 3.133333333

The y term is -8.333333333y.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333y + 17.36111111 + y2 = 3.133333333 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333y + y2 = 3.133333333 + 17.36111111

Combine like terms: 3.133333333 + 17.36111111 = 20.494444443
17.36111111 + -8.333333333y + y2 = 20.494444443

Factor a perfect square on the left side:
(y + -4.166666667)(y + -4.166666667) = 20.494444443

Calculate the square root of the right side: 4.527079019

Break this problem into two subproblems by setting 
(y + -4.166666667) equal to 4.527079019 and -4.527079019.


Subproblem 1
y + -4.166666667 = 4.527079019

Simplifying
y + -4.166666667 = 4.527079019

Reorder the terms:
-4.166666667 + y = 4.527079019

Solving
-4.166666667 + y = 4.527079019

Solving for variable 'y'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + y = 4.527079019 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + y = 4.527079019 + 4.166666667
y = 4.527079019 + 4.166666667

Combine like terms: 4.527079019 + 4.166666667 = 8.693745686
y = 8.693745686

Simplifying
y = 8.693745686


Subproblem 2
y + -4.166666667 = -4.527079019

Simplifying
y + -4.166666667 = -4.527079019

Reorder the terms:
-4.166666667 + y = -4.527079019

Solving
-4.166666667 + y = -4.527079019

Solving for variable 'y'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + y = -4.527079019 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + y = -4.527079019 + 4.166666667
y = -4.527079019 + 4.166666667

Combine like terms: -4.527079019 + 4.166666667 = -0.360412352
y = -0.360412352

Simplifying
y = -0.360412352


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.693745686, -0.360412352}

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