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

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

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

Reorder the terms:
5y(-2 + y) = 6 + -3y
(-2 * 5y + y * 5y) = 6 + -3y
(-10y + 5y2) = 6 + -3y

Solving
-10y + 5y2 = 6 + -3y

Solving for variable 'y'.

Reorder the terms:
-6 + -10y + 3y + 5y2 = 6 + -3y + -6 + 3y

Combine like terms: -10y + 3y = -7y
-6 + -7y + 5y2 = 6 + -3y + -6 + 3y

Reorder the terms:
-6 + -7y + 5y2 = 6 + -6 + -3y + 3y

Combine like terms: 6 + -6 = 0
-6 + -7y + 5y2 = 0 + -3y + 3y
-6 + -7y + 5y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-6 + -7y + 5y2 = 0

Factor a trinomial.
(-3 + -5y)(2 + -1y) = 0

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

Simplifying
-3 + -5y = 0

Solving
-3 + -5y = 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 + -5y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5y = 0 + 3
-5y = 0 + 3

Combine like terms: 0 + 3 = 3
-5y = 3

Divide each side by '-5'.
y = -0.6

Simplifying
y = -0.6
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-0.6, 2}