2y(y-3)-y(y+1)=-6

Solution for 2y(y-3)-y(y+1)=-6 equation:

Simplifying
2y(y + -3) + -1y(y + 1) = -6

Reorder the terms:
2y(-3 + y) + -1y(y + 1) = -6
(-3 * 2y + y * 2y) + -1y(y + 1) = -6
(-6y + 2y2) + -1y(y + 1) = -6

Reorder the terms:
-6y + 2y2 + -1y(1 + y) = -6
-6y + 2y2 + (1 * -1y + y * -1y) = -6
-6y + 2y2 + (-1y + -1y2) = -6

Reorder the terms:
-6y + -1y + 2y2 + -1y2 = -6

Combine like terms: -6y + -1y = -7y
-7y + 2y2 + -1y2 = -6

Combine like terms: 2y2 + -1y2 = 1y2
-7y + 1y2 = -6

Solving
-7y + 1y2 = -6

Solving for variable 'y'.

Reorder the terms:
6 + -7y + 1y2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -7y + 1y2 = 0

Factor a trinomial.
(1 + -1y)(6 + -1y) = 0

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {1, 6}