(y+1)(y+11)=(y+4)(y+7)

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Solution for (y+1)(y+11)=(y+4)(y+7) equation: 


Simplifying
(y + 1)(y + 11) = (y + 4)(y + 7)

Reorder the terms:
(1 + y)(y + 11) = (y + 4)(y + 7)

Reorder the terms:
(1 + y)(11 + y) = (y + 4)(y + 7)

Multiply (1 + y) * (11 + y)
(1(11 + y) + y(11 + y)) = (y + 4)(y + 7)
((11 * 1 + y * 1) + y(11 + y)) = (y + 4)(y + 7)
((11 + 1y) + y(11 + y)) = (y + 4)(y + 7)
(11 + 1y + (11 * y + y * y)) = (y + 4)(y + 7)
(11 + 1y + (11y + y2)) = (y + 4)(y + 7)

Combine like terms: 1y + 11y = 12y
(11 + 12y + y2) = (y + 4)(y + 7)

Reorder the terms:
11 + 12y + y2 = (4 + y)(y + 7)

Reorder the terms:
11 + 12y + y2 = (4 + y)(7 + y)

Multiply (4 + y) * (7 + y)
11 + 12y + y2 = (4(7 + y) + y(7 + y))
11 + 12y + y2 = ((7 * 4 + y * 4) + y(7 + y))
11 + 12y + y2 = ((28 + 4y) + y(7 + y))
11 + 12y + y2 = (28 + 4y + (7 * y + y * y))
11 + 12y + y2 = (28 + 4y + (7y + y2))

Combine like terms: 4y + 7y = 11y
11 + 12y + y2 = (28 + 11y + y2)

Add '-1y2' to each side of the equation.
11 + 12y + y2 + -1y2 = 28 + 11y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
11 + 12y + 0 = 28 + 11y + y2 + -1y2
11 + 12y = 28 + 11y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
11 + 12y = 28 + 11y + 0
11 + 12y = 28 + 11y

Solving
11 + 12y = 28 + 11y

Solving for variable 'y'.

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

Add '-11y' to each side of the equation.
11 + 12y + -11y = 28 + 11y + -11y

Combine like terms: 12y + -11y = 1y
11 + 1y = 28 + 11y + -11y

Combine like terms: 11y + -11y = 0
11 + 1y = 28 + 0
11 + 1y = 28

Add '-11' to each side of the equation.
11 + -11 + 1y = 28 + -11

Combine like terms: 11 + -11 = 0
0 + 1y = 28 + -11
1y = 28 + -11

Combine like terms: 28 + -11 = 17
1y = 17

Divide each side by '1'.
y = 17

Simplifying
y = 17

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