6y(2y-5)=29

Solution for 6y(2y-5)=29 equation:

Simplifying
6y(2y + -5) = 29

Reorder the terms:
6y(-5 + 2y) = 29
(-5 * 6y + 2y * 6y) = 29
(-30y + 12y2) = 29

Solving
-30y + 12y2 = 29

Solving for variable 'y'.

Reorder the terms:
-29 + -30y + 12y2 = 29 + -29

Combine like terms: 29 + -29 = 0
-29 + -30y + 12y2 = 0

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

Divide each side by '12'.
-2.416666667 + -2.5y + y2 = 0

Move the constant term to the right:

Add '2.416666667' to each side of the equation.
-2.416666667 + -2.5y + 2.416666667 + y2 = 0 + 2.416666667

Reorder the terms:
-2.416666667 + 2.416666667 + -2.5y + y2 = 0 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + -2.5y + y2 = 0 + 2.416666667
-2.5y + y2 = 0 + 2.416666667

Combine like terms: 0 + 2.416666667 = 2.416666667
-2.5y + y2 = 2.416666667

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = 2.416666667 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 2.416666667 + 1.5625

Combine like terms: 2.416666667 + 1.5625 = 3.979166667
1.5625 + -2.5y + y2 = 3.979166667

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 3.979166667

Calculate the square root of the right side: 1.994784867

Break this problem into two subproblems by setting 
(y + -1.25) equal to 1.994784867 and -1.994784867.

Subproblem 1
y + -1.25 = 1.994784867

Simplifying
y + -1.25 = 1.994784867

Reorder the terms:
-1.25 + y = 1.994784867

Solving
-1.25 + y = 1.994784867

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 1.994784867 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 1.994784867 + 1.25
y = 1.994784867 + 1.25

Combine like terms: 1.994784867 + 1.25 = 3.244784867
y = 3.244784867

Simplifying
y = 3.244784867

Subproblem 2
y + -1.25 = -1.994784867

Simplifying
y + -1.25 = -1.994784867

Reorder the terms:
-1.25 + y = -1.994784867

Solving
-1.25 + y = -1.994784867

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -1.994784867 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -1.994784867 + 1.25
y = -1.994784867 + 1.25

Combine like terms: -1.994784867 + 1.25 = -0.744784867
y = -0.744784867

Simplifying
y = -0.744784867

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.244784867, -0.744784867}