-y^2=-y-42

Solution for -y^2=-y-42 equation:

Simplifying
-1y2 = -1y + -42

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

Solving
-1y2 = -42 + -1y

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(7 + -1y)(6 + y) = 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 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

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