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

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

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

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

Reorder the terms:
6 + 6 + 6y + -2y = y * y

Combine like terms: 6 + 6 = 12
12 + 6y + -2y = y * y

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

Multiply y * y
12 + 4y = y2

Solving
12 + 4y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
12 + 4y + -1y2 = 0

Factor a trinomial.
(6 + -1y)(2 + y) = 0

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

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Solution
y = {6, -2}