4y(y-3)=6-2y

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

Simplifying
4y(y + -3) = 6 + -2y

Reorder the terms:
4y(-3 + y) = 6 + -2y
(-3 * 4y + y * 4y) = 6 + -2y
(-12y + 4y2) = 6 + -2y

Solving
-12y + 4y2 = 6 + -2y

Solving for variable 'y'.

Reorder the terms:
-6 + -12y + 2y + 4y2 = 6 + -2y + -6 + 2y

Combine like terms: -12y + 2y = -10y
-6 + -10y + 4y2 = 6 + -2y + -6 + 2y

Reorder the terms:
-6 + -10y + 4y2 = 6 + -6 + -2y + 2y

Combine like terms: 6 + -6 = 0
-6 + -10y + 4y2 = 0 + -2y + 2y
-6 + -10y + 4y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-6 + -10y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5y + 2y2) = 0

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

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

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

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

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

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-0.5, 3}