6y-4y(y-1)+6=

Solution for 6y-4y(y-1)+6= equation:

Simplifying
6y + -4y(y + -1) + 6 = 0

Reorder the terms:
6y + -4y(-1 + y) + 6 = 0
6y + (-1 * -4y + y * -4y) + 6 = 0
6y + (4y + -4y2) + 6 = 0

Reorder the terms:
6 + 6y + 4y + -4y2 = 0

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

Solving
6 + 10y + -4y2 = 0

Solving for variable 'y'.

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
y = {3, -0.5}