(5-2y)3y=5

Solution for (5-2y)3y=5 equation:

Simplifying
(5 + -2y) * 3y = 5

Reorder the terms for easier multiplication:
3y(5 + -2y) = 5
(5 * 3y + -2y * 3y) = 5
(15y + -6y2) = 5

Solving
15y + -6y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 15y + -6y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 15y + -6y2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.8333333333 + -2.5y + y2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -2.5y + -0.8333333333 + y2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -2.5y + y2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -2.5y + y2 = 0 + -0.8333333333
-2.5y + y2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-2.5y + y2 = -0.8333333333

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 = -0.8333333333 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = -0.8333333333 + 1.5625

Combine like terms: -0.8333333333 + 1.5625 = 0.7291666667
1.5625 + -2.5y + y2 = 0.7291666667

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 0.7291666667

Calculate the square root of the right side: 0.853912564

Break this problem into two subproblems by setting 
(y + -1.25) equal to 0.853912564 and -0.853912564.

Subproblem 1
y + -1.25 = 0.853912564

Simplifying
y + -1.25 = 0.853912564

Reorder the terms:
-1.25 + y = 0.853912564

Solving
-1.25 + y = 0.853912564

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 = 0.853912564 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 0.853912564 + 1.25
y = 0.853912564 + 1.25

Combine like terms: 0.853912564 + 1.25 = 2.103912564
y = 2.103912564

Simplifying
y = 2.103912564

Subproblem 2
y + -1.25 = -0.853912564

Simplifying
y + -1.25 = -0.853912564

Reorder the terms:
-1.25 + y = -0.853912564

Solving
-1.25 + y = -0.853912564

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 = -0.853912564 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -0.853912564 + 1.25
y = -0.853912564 + 1.25

Combine like terms: -0.853912564 + 1.25 = 0.396087436
y = 0.396087436

Simplifying
y = 0.396087436

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.103912564, 0.396087436}