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

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

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

Reorder the terms:
5(-3 + 2y) * 3y = 3

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

Multiply 5 * 3
15y(-3 + 2y) = 3
(-3 * 15y + 2y * 15y) = 3
(-45y + 30y2) = 3

Solving
-45y + 30y2 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + -45y + 30y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -45y + 30y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -15y + 10y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -15y + 10y2)' equal to zero and attempt to solve:

Simplifying
-1 + -15y + 10y2 = 0

Solving
-1 + -15y + 10y2 = 0

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

Divide each side by '10'.
-0.1 + -1.5y + y2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -1.5y + 0.1 + y2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -1.5y + y2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -1.5y + y2 = 0.0 + 0.1
-1.5y + y2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
-1.5y + y2 = 0.1

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 0.1 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = 0.1 + 0.5625

Combine like terms: 0.1 + 0.5625 = 0.6625
0.5625 + -1.5y + y2 = 0.6625

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 0.6625

Calculate the square root of the right side: 0.81394103

Break this problem into two subproblems by setting 
(y + -0.75) equal to 0.81394103 and -0.81394103.

Subproblem 1
y + -0.75 = 0.81394103

Simplifying
y + -0.75 = 0.81394103

Reorder the terms:
-0.75 + y = 0.81394103

Solving
-0.75 + y = 0.81394103

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = 0.81394103 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = 0.81394103 + 0.75
y = 0.81394103 + 0.75

Combine like terms: 0.81394103 + 0.75 = 1.56394103
y = 1.56394103

Simplifying
y = 1.56394103

Subproblem 2
y + -0.75 = -0.81394103

Simplifying
y + -0.75 = -0.81394103

Reorder the terms:
-0.75 + y = -0.81394103

Solving
-0.75 + y = -0.81394103

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = -0.81394103 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = -0.81394103 + 0.75
y = -0.81394103 + 0.75

Combine like terms: -0.81394103 + 0.75 = -0.06394103
y = -0.06394103

Simplifying
y = -0.06394103

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.56394103, -0.06394103}
Solution
y = {1.56394103, -0.06394103}