6y(y+3)=-2(3y-9)

Solution for 6y(y+3)=-2(3y-9) equation:

Simplifying
6y(y + 3) = -2(3y + -9)

Reorder the terms:
6y(3 + y) = -2(3y + -9)
(3 * 6y + y * 6y) = -2(3y + -9)
(18y + 6y2) = -2(3y + -9)

Reorder the terms:
18y + 6y2 = -2(-9 + 3y)
18y + 6y2 = (-9 * -2 + 3y * -2)
18y + 6y2 = (18 + -6y)

Solving
18y + 6y2 = 18 + -6y

Solving for variable 'y'.

Reorder the terms:
-18 + 18y + 6y + 6y2 = 18 + -6y + -18 + 6y

Combine like terms: 18y + 6y = 24y
-18 + 24y + 6y2 = 18 + -6y + -18 + 6y

Reorder the terms:
-18 + 24y + 6y2 = 18 + -18 + -6y + 6y

Combine like terms: 18 + -18 = 0
-18 + 24y + 6y2 = 0 + -6y + 6y
-18 + 24y + 6y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-18 + 24y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 4y + y2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + 4y + y2)' equal to zero and attempt to solve:

Simplifying
-3 + 4y + y2 = 0

Solving
-3 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 4y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4y + y2 = 0 + 3
4y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
4y + y2 = 3

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 3 + 4

Reorder the terms:
4 + 4y + y2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + 4y + y2 = 7

Factor a perfect square on the left side:
(y + 2)(y + 2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1
y + 2 = 2.645751311

Simplifying
y + 2 = 2.645751311

Reorder the terms:
2 + y = 2.645751311

Solving
2 + y = 2.645751311

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + y = 2.645751311 + -2
y = 2.645751311 + -2

Combine like terms: 2.645751311 + -2 = 0.645751311
y = 0.645751311

Simplifying
y = 0.645751311

Subproblem 2
y + 2 = -2.645751311

Simplifying
y + 2 = -2.645751311

Reorder the terms:
2 + y = -2.645751311

Solving
2 + y = -2.645751311

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + y = -2.645751311 + -2
y = -2.645751311 + -2

Combine like terms: -2.645751311 + -2 = -4.645751311
y = -4.645751311

Simplifying
y = -4.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.645751311, -4.645751311}
Solution
y = {0.645751311, -4.645751311}