-5y(4-6y)=3+3y-6y^2

Solution for -5y(4-6y)=3+3y-6y^2 equation:

Simplifying
-5y(4 + -6y) = 3 + 3y + -6y2
(4 * -5y + -6y * -5y) = 3 + 3y + -6y2
(-20y + 30y2) = 3 + 3y + -6y2

Solving
-20y + 30y2 = 3 + 3y + -6y2

Solving for variable 'y'.

Reorder the terms:
-3 + -20y + -3y + 30y2 + 6y2 = 3 + 3y + -6y2 + -3 + -3y + 6y2

Combine like terms: -20y + -3y = -23y
-3 + -23y + 30y2 + 6y2 = 3 + 3y + -6y2 + -3 + -3y + 6y2

Combine like terms: 30y2 + 6y2 = 36y2
-3 + -23y + 36y2 = 3 + 3y + -6y2 + -3 + -3y + 6y2

Reorder the terms:
-3 + -23y + 36y2 = 3 + -3 + 3y + -3y + -6y2 + 6y2

Combine like terms: 3 + -3 = 0
-3 + -23y + 36y2 = 0 + 3y + -3y + -6y2 + 6y2
-3 + -23y + 36y2 = 3y + -3y + -6y2 + 6y2

Combine like terms: 3y + -3y = 0
-3 + -23y + 36y2 = 0 + -6y2 + 6y2
-3 + -23y + 36y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
-3 + -23y + 36y2 = 0

Factor a trinomial.
(-1 + -9y)(3 + -4y) = 0

Subproblem 1
Set the factor '(-1 + -9y)' equal to zero and attempt to solve:

Simplifying
-1 + -9y = 0

Solving
-1 + -9y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -9y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9y = 0 + 1
-9y = 0 + 1

Combine like terms: 0 + 1 = 1
-9y = 1

Divide each side by '-9'.
y = -0.1111111111

Simplifying
y = -0.1111111111
Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 0

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

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

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

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

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {-0.1111111111, 0.75}