Solve A=left(y+5right)left(y-2right)-6left(y+5right)

$$A = \left( y+5 \right) \left( y-2 \right) -6 \left( y+5 \right)$$

Solve for A

$$A=\left(y-8\right)\left(y+5\right)$$

Solution Steps

Use the distributive property to multiply y+5 by y-2 and combine like terms.

$$A=y^{2}+3y-10-6\left(y+5\right)$$

Use the distributive property to multiply -6 by y+5.

$$A=y^{2}+3y-10-6y-30$$

Combine 3y and -6y to get -3y.

$$A=y^{2}-3y-10-30$$

Subtract 30 from -10 to get -40.

$$A=y^{2}-3y-40$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{4A+169}+3}{2}$$

$$y=\frac{\sqrt{4A+169}+3}{2}$$

Solve for y

$$y=\frac{-\sqrt{4A+169}+3}{2}$$

$$y=\frac{\sqrt{4A+169}+3}{2}\text{, }A\geq -\frac{169}{4}$$