y(2-y)=6-(y(y)+3y-4)

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Solution for y(2-y)=6-(y(y)+3y-4) equation: 


Simplifying
y(2 + -1y) = 6 + -1(y(y) + 3y + -4)
(2 * y + -1y * y) = 6 + -1(y(y) + 3y + -4)
(2y + -1y2) = 6 + -1(y(y) + 3y + -4)

Multiply y * y
2y + -1y2 = 6 + -1(y2 + 3y + -4)

Reorder the terms:
2y + -1y2 = 6 + -1(-4 + 3y + y2)
2y + -1y2 = 6 + (-4 * -1 + 3y * -1 + y2 * -1)
2y + -1y2 = 6 + (4 + -3y + -1y2)

Combine like terms: 6 + 4 = 10
2y + -1y2 = 10 + -3y + -1y2

Add 'y2' to each side of the equation.
2y + -1y2 + y2 = 10 + -3y + -1y2 + y2

Combine like terms: -1y2 + y2 = 0
2y + 0 = 10 + -3y + -1y2 + y2
2y = 10 + -3y + -1y2 + y2

Combine like terms: -1y2 + y2 = 0
2y = 10 + -3y + 0
2y = 10 + -3y

Solving
2y = 10 + -3y

Solving for variable 'y'.

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

Add '3y' to each side of the equation.
2y + 3y = 10 + -3y + 3y

Combine like terms: 2y + 3y = 5y
5y = 10 + -3y + 3y

Combine like terms: -3y + 3y = 0
5y = 10 + 0
5y = 10

Divide each side by '5'.
y = 2

Simplifying
y = 2

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