(3y-5)(y+4)-(y-3)(y-5)=

Solution for (3y-5)(y+4)-(y-3)(y-5)= equation:

Simplifying
(3y + -5)(y + 4) + -1(y + -3)(y + -5) = 0

Reorder the terms:
(-5 + 3y)(y + 4) + -1(y + -3)(y + -5) = 0

Reorder the terms:
(-5 + 3y)(4 + y) + -1(y + -3)(y + -5) = 0

Multiply (-5 + 3y) * (4 + y)
(-5(4 + y) + 3y * (4 + y)) + -1(y + -3)(y + -5) = 0
((4 * -5 + y * -5) + 3y * (4 + y)) + -1(y + -3)(y + -5) = 0
((-20 + -5y) + 3y * (4 + y)) + -1(y + -3)(y + -5) = 0
(-20 + -5y + (4 * 3y + y * 3y)) + -1(y + -3)(y + -5) = 0
(-20 + -5y + (12y + 3y2)) + -1(y + -3)(y + -5) = 0

Combine like terms: -5y + 12y = 7y
(-20 + 7y + 3y2) + -1(y + -3)(y + -5) = 0

Reorder the terms:
-20 + 7y + 3y2 + -1(-3 + y)(y + -5) = 0

Reorder the terms:
-20 + 7y + 3y2 + -1(-3 + y)(-5 + y) = 0

Multiply (-3 + y) * (-5 + y)
-20 + 7y + 3y2 + -1(-3(-5 + y) + y(-5 + y)) = 0
-20 + 7y + 3y2 + -1((-5 * -3 + y * -3) + y(-5 + y)) = 0
-20 + 7y + 3y2 + -1((15 + -3y) + y(-5 + y)) = 0
-20 + 7y + 3y2 + -1(15 + -3y + (-5 * y + y * y)) = 0
-20 + 7y + 3y2 + -1(15 + -3y + (-5y + y2)) = 0

Combine like terms: -3y + -5y = -8y
-20 + 7y + 3y2 + -1(15 + -8y + y2) = 0
-20 + 7y + 3y2 + (15 * -1 + -8y * -1 + y2 * -1) = 0
-20 + 7y + 3y2 + (-15 + 8y + -1y2) = 0

Reorder the terms:
-20 + -15 + 7y + 8y + 3y2 + -1y2 = 0

Combine like terms: -20 + -15 = -35
-35 + 7y + 8y + 3y2 + -1y2 = 0

Combine like terms: 7y + 8y = 15y
-35 + 15y + 3y2 + -1y2 = 0

Combine like terms: 3y2 + -1y2 = 2y2
-35 + 15y + 2y2 = 0

Solving
-35 + 15y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-17.5 + 7.5y + y2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 7.5y + 17.5 + y2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 7.5y + y2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 7.5y + y2 = 0 + 17.5
7.5y + y2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
7.5y + y2 = 17.5

The y term is 7.5y.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5y + 14.0625 + y2 = 17.5 + 14.0625

Reorder the terms:
14.0625 + 7.5y + y2 = 17.5 + 14.0625

Combine like terms: 17.5 + 14.0625 = 31.5625
14.0625 + 7.5y + y2 = 31.5625

Factor a perfect square on the left side:
(y + 3.75)(y + 3.75) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(y + 3.75) equal to 5.618051264 and -5.618051264.

Subproblem 1
y + 3.75 = 5.618051264

Simplifying
y + 3.75 = 5.618051264

Reorder the terms:
3.75 + y = 5.618051264

Solving
3.75 + y = 5.618051264

Solving for variable 'y'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + y = 5.618051264 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + y = 5.618051264 + -3.75
y = 5.618051264 + -3.75

Combine like terms: 5.618051264 + -3.75 = 1.868051264
y = 1.868051264

Simplifying
y = 1.868051264

Subproblem 2
y + 3.75 = -5.618051264

Simplifying
y + 3.75 = -5.618051264

Reorder the terms:
3.75 + y = -5.618051264

Solving
3.75 + y = -5.618051264

Solving for variable 'y'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + y = -5.618051264 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + y = -5.618051264 + -3.75
y = -5.618051264 + -3.75

Combine like terms: -5.618051264 + -3.75 = -9.368051264
y = -9.368051264

Simplifying
y = -9.368051264

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.868051264, -9.368051264}