3y(y-3)+5=3

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

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

Reorder the terms:
3y(-3 + y) + 5 = 3
(-3 * 3y + y * 3y) + 5 = 3
(-9y + 3y2) + 5 = 3

Reorder the terms:
5 + -9y + 3y2 = 3

Solving
5 + -9y + 3y2 = 3

Solving for variable 'y'.

Reorder the terms:
5 + -3 + -9y + 3y2 = 3 + -3

Combine like terms: 5 + -3 = 2
2 + -9y + 3y2 = 3 + -3

Combine like terms: 3 + -3 = 0
2 + -9y + 3y2 = 0

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

Divide each side by '3'.
0.6666666667 + -3y + y2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3y + -0.6666666667 + y2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3y + y2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3y + y2 = 0 + -0.6666666667
-3y + y2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3y + y2 = -0.6666666667

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -0.6666666667 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -0.6666666667 + 2.25

Combine like terms: -0.6666666667 + 2.25 = 1.5833333333
2.25 + -3y + y2 = 1.5833333333

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 1.5833333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.258305739 and -1.258305739.

Subproblem 1
y + -1.5 = 1.258305739

Simplifying
y + -1.5 = 1.258305739

Reorder the terms:
-1.5 + y = 1.258305739

Solving
-1.5 + y = 1.258305739

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.258305739 + 1.5
y = 1.258305739 + 1.5

Combine like terms: 1.258305739 + 1.5 = 2.758305739
y = 2.758305739

Simplifying
y = 2.758305739

Subproblem 2
y + -1.5 = -1.258305739

Simplifying
y + -1.5 = -1.258305739

Reorder the terms:
-1.5 + y = -1.258305739

Solving
-1.5 + y = -1.258305739

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.258305739 + 1.5
y = -1.258305739 + 1.5

Combine like terms: -1.258305739 + 1.5 = 0.241694261
y = 0.241694261

Simplifying
y = 0.241694261

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.758305739, 0.241694261}