(3+x)(y+5)=(x+2)(y+8)

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Solution for (3+x)(y+5)=(x+2)(y+8) equation:


Simplifying
(3 + x)(y + 5) = (x + 2)(y + 8)

Reorder the terms:
(3 + x)(5 + y) = (x + 2)(y + 8)

Multiply (3 + x) * (5 + y)
(3(5 + y) + x(5 + y)) = (x + 2)(y + 8)
((5 * 3 + y * 3) + x(5 + y)) = (x + 2)(y + 8)
((15 + 3y) + x(5 + y)) = (x + 2)(y + 8)
(15 + 3y + (5 * x + y * x)) = (x + 2)(y + 8)
(15 + 3y + (5x + xy)) = (x + 2)(y + 8)

Reorder the terms:
(15 + 5x + xy + 3y) = (x + 2)(y + 8)
(15 + 5x + xy + 3y) = (x + 2)(y + 8)

Reorder the terms:
15 + 5x + xy + 3y = (2 + x)(y + 8)

Reorder the terms:
15 + 5x + xy + 3y = (2 + x)(8 + y)

Multiply (2 + x) * (8 + y)
15 + 5x + xy + 3y = (2(8 + y) + x(8 + y))
15 + 5x + xy + 3y = ((8 * 2 + y * 2) + x(8 + y))
15 + 5x + xy + 3y = ((16 + 2y) + x(8 + y))
15 + 5x + xy + 3y = (16 + 2y + (8 * x + y * x))
15 + 5x + xy + 3y = (16 + 2y + (8x + xy))

Reorder the terms:
15 + 5x + xy + 3y = (16 + 8x + xy + 2y)
15 + 5x + xy + 3y = (16 + 8x + xy + 2y)

Add '-1xy' to each side of the equation.
15 + 5x + xy + -1xy + 3y = 16 + 8x + xy + -1xy + 2y

Combine like terms: xy + -1xy = 0
15 + 5x + 0 + 3y = 16 + 8x + xy + -1xy + 2y
15 + 5x + 3y = 16 + 8x + xy + -1xy + 2y

Combine like terms: xy + -1xy = 0
15 + 5x + 3y = 16 + 8x + 0 + 2y
15 + 5x + 3y = 16 + 8x + 2y

Solving
15 + 5x + 3y = 16 + 8x + 2y

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
15 + 5x + -8x + 3y = 16 + 8x + -8x + 2y

Combine like terms: 5x + -8x = -3x
15 + -3x + 3y = 16 + 8x + -8x + 2y

Combine like terms: 8x + -8x = 0
15 + -3x + 3y = 16 + 0 + 2y
15 + -3x + 3y = 16 + 2y

Add '-15' to each side of the equation.
15 + -3x + -15 + 3y = 16 + -15 + 2y

Reorder the terms:
15 + -15 + -3x + 3y = 16 + -15 + 2y

Combine like terms: 15 + -15 = 0
0 + -3x + 3y = 16 + -15 + 2y
-3x + 3y = 16 + -15 + 2y

Combine like terms: 16 + -15 = 1
-3x + 3y = 1 + 2y

Add '-3y' to each side of the equation.
-3x + 3y + -3y = 1 + 2y + -3y

Combine like terms: 3y + -3y = 0
-3x + 0 = 1 + 2y + -3y
-3x = 1 + 2y + -3y

Combine like terms: 2y + -3y = -1y
-3x = 1 + -1y

Divide each side by '-3'.
x = -0.3333333333 + 0.3333333333y

Simplifying
x = -0.3333333333 + 0.3333333333y

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