4(y+1)+y=5y(y-1)+9

Solution for 4(y+1)+y=5y(y-1)+9 equation:

Simplifying
4(y + 1) + y = 5y(y + -1) + 9

Reorder the terms:
4(1 + y) + y = 5y(y + -1) + 9
(1 * 4 + y * 4) + y = 5y(y + -1) + 9
(4 + 4y) + y = 5y(y + -1) + 9

Combine like terms: 4y + y = 5y
4 + 5y = 5y(y + -1) + 9

Reorder the terms:
4 + 5y = 5y(-1 + y) + 9
4 + 5y = (-1 * 5y + y * 5y) + 9
4 + 5y = (-5y + 5y2) + 9

Reorder the terms:
4 + 5y = 9 + -5y + 5y2

Solving
4 + 5y = 9 + -5y + 5y2

Solving for variable 'y'.

Reorder the terms:
4 + -9 + 5y + 5y + -5y2 = 9 + -5y + 5y2 + -9 + 5y + -5y2

Combine like terms: 4 + -9 = -5
-5 + 5y + 5y + -5y2 = 9 + -5y + 5y2 + -9 + 5y + -5y2

Combine like terms: 5y + 5y = 10y
-5 + 10y + -5y2 = 9 + -5y + 5y2 + -9 + 5y + -5y2

Reorder the terms:
-5 + 10y + -5y2 = 9 + -9 + -5y + 5y + 5y2 + -5y2

Combine like terms: 9 + -9 = 0
-5 + 10y + -5y2 = 0 + -5y + 5y + 5y2 + -5y2
-5 + 10y + -5y2 = -5y + 5y + 5y2 + -5y2

Combine like terms: -5y + 5y = 0
-5 + 10y + -5y2 = 0 + 5y2 + -5y2
-5 + 10y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-5 + 10y + -5y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 2y + -1y2) = 0

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

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

Simplifying
-1 + y = 0

Solving
-1 + y = 0

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

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

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

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {1, 1}