-5y(3y-6)+3(2y+8)=

Solution for -5y(3y-6)+3(2y+8)= equation:

Simplifying
-5y(3y + -6) + 3(2y + 8) = 0

Reorder the terms:
-5y(-6 + 3y) + 3(2y + 8) = 0
(-6 * -5y + 3y * -5y) + 3(2y + 8) = 0
(30y + -15y2) + 3(2y + 8) = 0

Reorder the terms:
30y + -15y2 + 3(8 + 2y) = 0
30y + -15y2 + (8 * 3 + 2y * 3) = 0
30y + -15y2 + (24 + 6y) = 0

Reorder the terms:
24 + 30y + 6y + -15y2 = 0

Combine like terms: 30y + 6y = 36y
24 + 36y + -15y2 = 0

Solving
24 + 36y + -15y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 12y + -5y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + 12y + -5y2)' equal to zero and attempt to solve:

Simplifying
8 + 12y + -5y2 = 0

Solving
8 + 12y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.6 + -2.4y + y2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -2.4y + 1.6 + y2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -2.4y + y2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -2.4y + y2 = 0 + 1.6
-2.4y + y2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-2.4y + y2 = 1.6

The y term is -2.4y.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4y + 1.44 + y2 = 1.6 + 1.44

Reorder the terms:
1.44 + -2.4y + y2 = 1.6 + 1.44

Combine like terms: 1.6 + 1.44 = 3.04
1.44 + -2.4y + y2 = 3.04

Factor a perfect square on the left side:
(y + -1.2)(y + -1.2) = 3.04

Calculate the square root of the right side: 1.743559577

Break this problem into two subproblems by setting 
(y + -1.2) equal to 1.743559577 and -1.743559577.

Subproblem 1
y + -1.2 = 1.743559577

Simplifying
y + -1.2 = 1.743559577

Reorder the terms:
-1.2 + y = 1.743559577

Solving
-1.2 + y = 1.743559577

Solving for variable 'y'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + y = 1.743559577 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + y = 1.743559577 + 1.2
y = 1.743559577 + 1.2

Combine like terms: 1.743559577 + 1.2 = 2.943559577
y = 2.943559577

Simplifying
y = 2.943559577

Subproblem 2
y + -1.2 = -1.743559577

Simplifying
y + -1.2 = -1.743559577

Reorder the terms:
-1.2 + y = -1.743559577

Solving
-1.2 + y = -1.743559577

Solving for variable 'y'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + y = -1.743559577 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + y = -1.743559577 + 1.2
y = -1.743559577 + 1.2

Combine like terms: -1.743559577 + 1.2 = -0.543559577
y = -0.543559577

Simplifying
y = -0.543559577

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.943559577, -0.543559577}
Solution
y = {2.943559577, -0.543559577}