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

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


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

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

Reorder the terms for easier multiplication:
y(5 + y) = (y + 1)((y + 5) + -2)
(5 * y + y * y) = (y + 1)((y + 5) + -2)
(5y + y2) = (y + 1)((y + 5) + -2)

Reorder the terms:
5y + y2 = (1 + y)((y + 5) + -2)

Reorder the terms:
5y + y2 = (1 + y)((5 + y) + -2)

Remove parenthesis around (5 + y)
5y + y2 = (1 + y)(5 + y + -2)

Reorder the terms:
5y + y2 = (1 + y)(5 + -2 + y)

Combine like terms: 5 + -2 = 3
5y + y2 = (1 + y)(3 + y)

Multiply (1 + y) * (3 + y)
5y + y2 = (1(3 + y) + y(3 + y))
5y + y2 = ((3 * 1 + y * 1) + y(3 + y))
5y + y2 = ((3 + 1y) + y(3 + y))
5y + y2 = (3 + 1y + (3 * y + y * y))
5y + y2 = (3 + 1y + (3y + y2))

Combine like terms: 1y + 3y = 4y
5y + y2 = (3 + 4y + y2)

Add '-1y2' to each side of the equation.
5y + y2 + -1y2 = 3 + 4y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5y + 0 = 3 + 4y + y2 + -1y2
5y = 3 + 4y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5y = 3 + 4y + 0
5y = 3 + 4y

Solving
5y = 3 + 4y

Solving for variable 'y'.

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

Add '-4y' to each side of the equation.
5y + -4y = 3 + 4y + -4y

Combine like terms: 5y + -4y = 1y
1y = 3 + 4y + -4y

Combine like terms: 4y + -4y = 0
1y = 3 + 0
1y = 3

Divide each side by '1'.
y = 3

Simplifying
y = 3

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