"To calculate: The solution of the equation 3y2−4y=8−6y" was answered by our community

gonjenjemeb

Answered question

2021-11-19

To calculate: The solution of the equation

3 y^{2} - 4 y = 8 - 6 y

Blanche McClain

Beginner2021-11-20Added 15 answers

Consider the equation,

3 y^{2} - 4 y = 8 - 6 y

Set one side of the equation equal to zero.

3 y^{2} - 4 y - (8 - 6 y) = 0

3 y^{2} - 4 y - 8 + 6 y = 0

3 y^{2} + 2 y - 8 = 0 y

Make the factors of the equation.

3 y^{2} + (6 - 4) y - 8 = 0

(3 y^{2} + 6 y) + (- 4 y - 8) = 0

3 y (y + 2) - 4 (y + 2) = 0 y

(3 y - 4) (y + 2) = 0

Use the zero-product property.

3 y - 4 = 0

y + 2 = 0

3 y = 4

y = - 2

y = \frac{4}{3}

Check the solution

y = \frac{4}{3}

in the equation

3 y^{2} - 4 y = 8 - 6 y

3 {(\frac{4}{3})}^{2} - 4 (\frac{4}{3}) \overset{?}{=} 8 - 6 (\frac{4}{3})

3 (\frac{16}{9}) - \frac{16}{3} \overset{?}{=} 8 - \frac{24}{3}

\frac{16}{3} - \frac{16}{3} \overset{?}{=} \frac{24 - 24}{3}

0 = 0

So, the answer is verified.
Check the solution

y = — 2

in the equation

3 y^{2} - 4 y = 8 - 6 y

3 {(- 2)}^{2} - 4 (- 2) \overset{?}{=} 8 - 6 (- 2)

3 (4) + 8 \overset{?}{=} 8 + 12

12 + 8 \overset{?}{=} 20

20 = 20

So, the answer is verified.
Therefore, thesolution of the equation

3 y^{2} - 4 y = 8 - 6 y

{\frac{4}{3}, - 2}

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