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

Solution for (3y-4)(y-1)-y(y+3)=0 equation:

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

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

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

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

Combine like terms: -4y + -3y = -7y
(4 + -7y + 3y2) + -1y(y + 3) = 0

Reorder the terms:
4 + -7y + 3y2 + -1y(3 + y) = 0
4 + -7y + 3y2 + (3 * -1y + y * -1y) = 0
4 + -7y + 3y2 + (-3y + -1y2) = 0

Reorder the terms:
4 + -7y + -3y + 3y2 + -1y2 = 0

Combine like terms: -7y + -3y = -10y
4 + -10y + 3y2 + -1y2 = 0

Combine like terms: 3y2 + -1y2 = 2y2
4 + -10y + 2y2 = 0

Solving
4 + -10y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -5y + y2)' equal to zero and attempt to solve:

Simplifying
2 + -5y + y2 = 0

Solving
2 + -5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -5y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y + y2 = 0 + -2
-5y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5y + y2 = -2

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 = -2 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5y + y2 = 4.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(y + -2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
y + -2.5 = 2.061552813

Simplifying
y + -2.5 = 2.061552813

Reorder the terms:
-2.5 + y = 2.061552813

Solving
-2.5 + y = 2.061552813

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 = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 2.061552813 + 2.5
y = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
y = 4.561552813

Simplifying
y = 4.561552813

Subproblem 2
y + -2.5 = -2.061552813

Simplifying
y + -2.5 = -2.061552813

Reorder the terms:
-2.5 + y = -2.061552813

Solving
-2.5 + y = -2.061552813

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 = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -2.061552813 + 2.5
y = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
y = 0.438447187

Simplifying
y = 0.438447187

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.561552813, 0.438447187}
Solution
y = {4.561552813, 0.438447187}