3y-y=y(1-y)+42

Solution for 3y-y=y(1-y)+42 equation:

Simplifying
3y + -1y = y(1 + -1y) + 42

Combine like terms: 3y + -1y = 2y
2y = y(1 + -1y) + 42
2y = (1 * y + -1y * y) + 42
2y = (1y + -1y2) + 42

Reorder the terms:
2y = 42 + 1y + -1y2

Solving
2y = 42 + 1y + -1y2

Solving for variable 'y'.

Reorder the terms:
-42 + 2y + -1y + y2 = 42 + 1y + -1y2 + -42 + -1y + y2

Combine like terms: 2y + -1y = 1y
-42 + 1y + y2 = 42 + 1y + -1y2 + -42 + -1y + y2

Reorder the terms:
-42 + 1y + y2 = 42 + -42 + 1y + -1y + -1y2 + y2

Combine like terms: 42 + -42 = 0
-42 + 1y + y2 = 0 + 1y + -1y + -1y2 + y2
-42 + 1y + y2 = 1y + -1y + -1y2 + y2

Combine like terms: 1y + -1y = 0
-42 + 1y + y2 = 0 + -1y2 + y2
-42 + 1y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-42 + 1y + y2 = 0

Factor a trinomial.
(-7 + -1y)(6 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

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

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

Divide each side by '-1'.
y = -7

Simplifying
y = -7
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 = {-7, 6}