(y+5)(y-1)=2y-5

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Solution for (y+5)(y-1)=2y-5 equation: 


Simplifying
(y + 5)(y + -1) = 2y + -5

Reorder the terms:
(5 + y)(y + -1) = 2y + -5

Reorder the terms:
(5 + y)(-1 + y) = 2y + -5

Multiply (5 + y) * (-1 + y)
(5(-1 + y) + y(-1 + y)) = 2y + -5
((-1 * 5 + y * 5) + y(-1 + y)) = 2y + -5
((-5 + 5y) + y(-1 + y)) = 2y + -5
(-5 + 5y + (-1 * y + y * y)) = 2y + -5
(-5 + 5y + (-1y + y2)) = 2y + -5

Combine like terms: 5y + -1y = 4y
(-5 + 4y + y2) = 2y + -5

Reorder the terms:
-5 + 4y + y2 = -5 + 2y

Add '5' to each side of the equation.
-5 + 4y + 5 + y2 = -5 + 5 + 2y

Reorder the terms:
-5 + 5 + 4y + y2 = -5 + 5 + 2y

Combine like terms: -5 + 5 = 0
0 + 4y + y2 = -5 + 5 + 2y
4y + y2 = -5 + 5 + 2y

Combine like terms: -5 + 5 = 0
4y + y2 = 0 + 2y
4y + y2 = 2y

Solving
4y + y2 = 2y

Solving for variable 'y'.

Reorder the terms:
4y + -2y + y2 = 2y + -2y

Combine like terms: 4y + -2y = 2y
2y + y2 = 2y + -2y

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

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


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {0, -2}

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