(3y+2)(4y)=30

Solution for (3y+2)(4y)=30 equation:

Simplifying
(3y + 2)(4y) = 30

Reorder the terms:
(2 + 3y)(4y) = 30

Remove parenthesis around (4y)
(2 + 3y) * 4y = 30

Reorder the terms for easier multiplication:
4y(2 + 3y) = 30
(2 * 4y + 3y * 4y) = 30
(8y + 12y2) = 30

Solving
8y + 12y2 = 30

Solving for variable 'y'.

Reorder the terms:
-30 + 8y + 12y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 8y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 4y + 6y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 4y + 6y2)' equal to zero and attempt to solve:

Simplifying
-15 + 4y + 6y2 = 0

Solving
-15 + 4y + 6y2 = 0

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

Divide each side by '6'.
-2.5 + 0.6666666667y + y2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.6666666667y + 2.5 + y2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.6666666667y + y2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.6666666667y + y2 = 0 + 2.5
0.6666666667y + y2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.6666666667y + y2 = 2.5

The y term is 0.6666666667y.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667y + 0.1111111112 + y2 = 2.5 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667y + y2 = 2.5 + 0.1111111112

Combine like terms: 2.5 + 0.1111111112 = 2.6111111112
0.1111111112 + 0.6666666667y + y2 = 2.6111111112

Factor a perfect square on the left side:
(y + 0.3333333334)(y + 0.3333333334) = 2.6111111112

Calculate the square root of the right side: 1.615893286

Break this problem into two subproblems by setting 
(y + 0.3333333334) equal to 1.615893286 and -1.615893286.

Subproblem 1
y + 0.3333333334 = 1.615893286

Simplifying
y + 0.3333333334 = 1.615893286

Reorder the terms:
0.3333333334 + y = 1.615893286

Solving
0.3333333334 + y = 1.615893286

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = 1.615893286 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = 1.615893286 + -0.3333333334
y = 1.615893286 + -0.3333333334

Combine like terms: 1.615893286 + -0.3333333334 = 1.2825599526
y = 1.2825599526

Simplifying
y = 1.2825599526

Subproblem 2
y + 0.3333333334 = -1.615893286

Simplifying
y + 0.3333333334 = -1.615893286

Reorder the terms:
0.3333333334 + y = -1.615893286

Solving
0.3333333334 + y = -1.615893286

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = -1.615893286 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = -1.615893286 + -0.3333333334
y = -1.615893286 + -0.3333333334

Combine like terms: -1.615893286 + -0.3333333334 = -1.9492266194
y = -1.9492266194

Simplifying
y = -1.9492266194

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.2825599526, -1.9492266194}
Solution
y = {1.2825599526, -1.9492266194}