-15y^2+75y=25

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Solution for -15y^2+75y=25 equation: 


Simplifying
-15y2 + 75y = 25

Reorder the terms:
75y + -15y2 = 25

Solving
75y + -15y2 = 25

Solving for variable 'y'.

Reorder the terms:
-25 + 75y + -15y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 75y + -15y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 15y + -3y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + 15y + -3y2)' equal to zero and attempt to solve:

Simplifying
-5 + 15y + -3y2 = 0

Solving
-5 + 15y + -3y2 = 0

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

Divide each side by '-3'.
1.666666667 + -5y + y2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -5y + -1.666666667 + y2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -5y + y2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -5y + y2 = 0 + -1.666666667
-5y + y2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-5y + y2 = -1.666666667

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -1.666666667 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -1.666666667 + 6.25

Combine like terms: -1.666666667 + 6.25 = 4.583333333
6.25 + -5y + y2 = 4.583333333

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(y + -2.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
y + -2.5 = 2.140872096

Simplifying
y + -2.5 = 2.140872096

Reorder the terms:
-2.5 + y = 2.140872096

Solving
-2.5 + y = 2.140872096

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 2.140872096 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 2.140872096 + 2.5
y = 2.140872096 + 2.5

Combine like terms: 2.140872096 + 2.5 = 4.640872096
y = 4.640872096

Simplifying
y = 4.640872096


Subproblem 2
y + -2.5 = -2.140872096

Simplifying
y + -2.5 = -2.140872096

Reorder the terms:
-2.5 + y = -2.140872096

Solving
-2.5 + y = -2.140872096

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -2.140872096 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -2.140872096 + 2.5
y = -2.140872096 + 2.5

Combine like terms: -2.140872096 + 2.5 = 0.359127904
y = 0.359127904

Simplifying
y = 0.359127904


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.640872096, 0.359127904}
Solution
y = {4.640872096, 0.359127904}

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