Solve 2y^2+9(y-2)=(2y-3)(y+6)

$$2 y ^ { 2 } + 9 ( y - 2 ) = ( 2 y - 3 ) ( y + 6 )$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 9 by y-2.

$$2y^{2}+9y-18=\left(2y-3\right)\left(y+6\right)$$

Use the distributive property to multiply 2y-3 by y+6 and combine like terms.

$$2y^{2}+9y-18=2y^{2}+9y-18$$

Subtract 2y^{2} from both sides.

$$2y^{2}+9y-18-2y^{2}=9y-18$$

Combine 2y^{2} and -2y^{2} to get 0.

$$9y-18=9y-18$$

Subtract 9y from both sides.

$$9y-18-9y=-18$$

Combine 9y and -9y to get 0.

$$-18=-18$$

Compare -18 and -18.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for y

$$y\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 9 by y-2.

$$2y^{2}+9y-18=\left(2y-3\right)\left(y+6\right)$$

Use the distributive property to multiply 2y-3 by y+6 and combine like terms.

$$2y^{2}+9y-18=2y^{2}+9y-18$$

Subtract 2y^{2} from both sides.

$$2y^{2}+9y-18-2y^{2}=9y-18$$

Combine 2y^{2} and -2y^{2} to get 0.

$$9y-18=9y-18$$

Subtract 9y from both sides.

$$9y-18-9y=-18$$

Combine 9y and -9y to get 0.

$$-18=-18$$

Compare -18 and -18.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$