(3y-1)(2+y)=y(2+3y)

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Solution for (3y-1)(2+y)=y(2+3y) equation:


Simplifying
(3y + -1)(2 + y) = y(2 + 3y)

Reorder the terms:
(-1 + 3y)(2 + y) = y(2 + 3y)

Multiply (-1 + 3y) * (2 + y)
(-1(2 + y) + 3y * (2 + y)) = y(2 + 3y)
((2 * -1 + y * -1) + 3y * (2 + y)) = y(2 + 3y)
((-2 + -1y) + 3y * (2 + y)) = y(2 + 3y)
(-2 + -1y + (2 * 3y + y * 3y)) = y(2 + 3y)
(-2 + -1y + (6y + 3y2)) = y(2 + 3y)

Combine like terms: -1y + 6y = 5y
(-2 + 5y + 3y2) = y(2 + 3y)
-2 + 5y + 3y2 = (2 * y + 3y * y)
-2 + 5y + 3y2 = (2y + 3y2)

Add '-3y2' to each side of the equation.
-2 + 5y + 3y2 + -3y2 = 2y + 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-2 + 5y + 0 = 2y + 3y2 + -3y2
-2 + 5y = 2y + 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-2 + 5y = 2y + 0
-2 + 5y = 2y

Solving
-2 + 5y = 2y

Solving for variable 'y'.

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

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

Combine like terms: 5y + -2y = 3y
-2 + 3y = 2y + -2y

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

Add '2' to each side of the equation.
-2 + 2 + 3y = 0 + 2

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

Combine like terms: 0 + 2 = 2
3y = 2

Divide each side by '3'.
y = 0.6666666667

Simplifying
y = 0.6666666667

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