y^2-4y-16=-6y-1

Solution for y^2-4y-16=-6y-1 equation:

Simplifying
y2 + -4y + -16 = -6y + -1

Reorder the terms:
-16 + -4y + y2 = -6y + -1

Reorder the terms:
-16 + -4y + y2 = -1 + -6y

Solving
-16 + -4y + y2 = -1 + -6y

Solving for variable 'y'.

Reorder the terms:
-16 + 1 + -4y + 6y + y2 = -1 + -6y + 1 + 6y

Combine like terms: -16 + 1 = -15
-15 + -4y + 6y + y2 = -1 + -6y + 1 + 6y

Combine like terms: -4y + 6y = 2y
-15 + 2y + y2 = -1 + -6y + 1 + 6y

Reorder the terms:
-15 + 2y + y2 = -1 + 1 + -6y + 6y

Combine like terms: -1 + 1 = 0
-15 + 2y + y2 = 0 + -6y + 6y
-15 + 2y + y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-15 + 2y + y2 = 0

Factor a trinomial.
(-5 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5
Subproblem 2
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
Solution
y = {-5, 3}