15y^2-18y-25=0

Solution for 15y^2-18y-25=0 equation:

Simplifying
15y2 + -18y + -25 = 0

Reorder the terms:
-25 + -18y + 15y2 = 0

Solving
-25 + -18y + 15y2 = 0

Solving for variable 'y'.

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

Divide each side by '15'.
-1.666666667 + -1.2y + y2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1.2y + 1.666666667 + y2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1.2y + y2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.2y + y2 = 0 + 1.666666667
-1.2y + y2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1.2y + y2 = 1.666666667

The y term is -1.2y.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2y + 0.36 + y2 = 1.666666667 + 0.36

Reorder the terms:
0.36 + -1.2y + y2 = 1.666666667 + 0.36

Combine like terms: 1.666666667 + 0.36 = 2.026666667
0.36 + -1.2y + y2 = 2.026666667

Factor a perfect square on the left side:
(y + -0.6)(y + -0.6) = 2.026666667

Calculate the square root of the right side: 1.423610434

Break this problem into two subproblems by setting 
(y + -0.6) equal to 1.423610434 and -1.423610434.

Subproblem 1
y + -0.6 = 1.423610434

Simplifying
y + -0.6 = 1.423610434

Reorder the terms:
-0.6 + y = 1.423610434

Solving
-0.6 + y = 1.423610434

Solving for variable 'y'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + y = 1.423610434 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + y = 1.423610434 + 0.6
y = 1.423610434 + 0.6

Combine like terms: 1.423610434 + 0.6 = 2.023610434
y = 2.023610434

Simplifying
y = 2.023610434

Subproblem 2
y + -0.6 = -1.423610434

Simplifying
y + -0.6 = -1.423610434

Reorder the terms:
-0.6 + y = -1.423610434

Solving
-0.6 + y = -1.423610434

Solving for variable 'y'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + y = -1.423610434 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + y = -1.423610434 + 0.6
y = -1.423610434 + 0.6

Combine like terms: -1.423610434 + 0.6 = -0.823610434
y = -0.823610434

Simplifying
y = -0.823610434

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.023610434, -0.823610434}