What is the answer to 2x(x-1)y+3(x-1)y-y=0 ?

The answer to 2x(x-1)y+3(x-1)y-y=0 is y=0,x=(-1+sqrt(33))/4 ,x=(-1-sqrt(33))/4

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2x(x-1)y+3(x-1)y-y=0

2 x (x - 1) y + 3 (x - 1) y - y = 0

y = 0, x = \frac{- 1 + 33}{4}, x = \frac{- 1 - 33}{4}

Decimal Notation

y = 0, x = 1.18614 \dots, x = - 1.68614 \dots

Solution steps

2 x (x - 1) y + 3 (x - 1) y - y = 0

Factor

2 x (x - 1) y + 3 (x - 1) y - y : y (2 x^{2} + x - 4)

y (2 x^{2} + x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or 2 x^{2} + x - 4 = 0

y = 0

Solve

2 x^{2} + x - 4 = 0 : x = \frac{- 1 + 33}{4}, x = \frac{- 1 - 33}{4}

The solutions are

y = 0, x = \frac{- 1 + 33}{4}, x = \frac{- 1 - 33}{4}

x d 3 y d x 3 - (d y d x) 4 + y = 0

(x + 3) (y - 4) = 0

co x = 0

a \cdot b = 0, a = 0 or b = 0

2 x e^{- y} = 0

What is the answer to 2x(x-1)y+3(x-1)y-y=0 ?
The answer to 2x(x-1)y+3(x-1)y-y=0 is y=0,x=(-1+sqrt(33))/4 ,x=(-1-sqrt(33))/4