y(4y-6)=13(-y+1)

Solution for y(4y-6)=13(-y+1) equation:

Simplifying
y(4y + -6) = 13(-1y + 1)

Reorder the terms:
y(-6 + 4y) = 13(-1y + 1)
(-6 * y + 4y * y) = 13(-1y + 1)
(-6y + 4y2) = 13(-1y + 1)

Reorder the terms:
-6y + 4y2 = 13(1 + -1y)
-6y + 4y2 = (1 * 13 + -1y * 13)
-6y + 4y2 = (13 + -13y)

Solving
-6y + 4y2 = 13 + -13y

Solving for variable 'y'.

Reorder the terms:
-13 + -6y + 13y + 4y2 = 13 + -13y + -13 + 13y

Combine like terms: -6y + 13y = 7y
-13 + 7y + 4y2 = 13 + -13y + -13 + 13y

Reorder the terms:
-13 + 7y + 4y2 = 13 + -13 + -13y + 13y

Combine like terms: 13 + -13 = 0
-13 + 7y + 4y2 = 0 + -13y + 13y
-13 + 7y + 4y2 = -13y + 13y

Combine like terms: -13y + 13y = 0
-13 + 7y + 4y2 = 0

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

Divide each side by '4'.
-3.25 + 1.75y + y2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 1.75y + 3.25 + y2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 1.75y + y2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 1.75y + y2 = 0 + 3.25
1.75y + y2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
1.75y + y2 = 3.25

The y term is 1.75y.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75y + 0.765625 + y2 = 3.25 + 0.765625

Reorder the terms:
0.765625 + 1.75y + y2 = 3.25 + 0.765625

Combine like terms: 3.25 + 0.765625 = 4.015625
0.765625 + 1.75y + y2 = 4.015625

Factor a perfect square on the left side:
(y + 0.875)(y + 0.875) = 4.015625

Calculate the square root of the right side: 2.003902443

Break this problem into two subproblems by setting 
(y + 0.875) equal to 2.003902443 and -2.003902443.

Subproblem 1
y + 0.875 = 2.003902443

Simplifying
y + 0.875 = 2.003902443

Reorder the terms:
0.875 + y = 2.003902443

Solving
0.875 + y = 2.003902443

Solving for variable 'y'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + y = 2.003902443 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + y = 2.003902443 + -0.875
y = 2.003902443 + -0.875

Combine like terms: 2.003902443 + -0.875 = 1.128902443
y = 1.128902443

Simplifying
y = 1.128902443

Subproblem 2
y + 0.875 = -2.003902443

Simplifying
y + 0.875 = -2.003902443

Reorder the terms:
0.875 + y = -2.003902443

Solving
0.875 + y = -2.003902443

Solving for variable 'y'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + y = -2.003902443 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + y = -2.003902443 + -0.875
y = -2.003902443 + -0.875

Combine like terms: -2.003902443 + -0.875 = -2.878902443
y = -2.878902443

Simplifying
y = -2.878902443

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.128902443, -2.878902443}