16(y-1)=y(y+8)

Solution for 16(y-1)=y(y+8) equation:

Simplifying
16(y + -1) = y(y + 8)

Reorder the terms:
16(-1 + y) = y(y + 8)
(-1 * 16 + y * 16) = y(y + 8)
(-16 + 16y) = y(y + 8)

Reorder the terms:
-16 + 16y = y(8 + y)
-16 + 16y = (8 * y + y * y)
-16 + 16y = (8y + y2)

Solving
-16 + 16y = 8y + y2

Solving for variable 'y'.

Combine like terms: 16y + -8y = 8y
-16 + 8y + -1y2 = 8y + y2 + -8y + -1y2

Reorder the terms:
-16 + 8y + -1y2 = 8y + -8y + y2 + -1y2

Combine like terms: 8y + -8y = 0
-16 + 8y + -1y2 = 0 + y2 + -1y2
-16 + 8y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-16 + 8y + -1y2 = 0

Factor a trinomial.
(-4 + y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 0

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

Add '4' to each side of the equation.
-4 + 4 + y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + y = 0 + 4
y = 0 + 4

Combine like terms: 0 + 4 = 4
y = 4

Simplifying
y = 4
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

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

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

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {4, 4}