Solve 4y+2/5y^2+9y+4/5y-y^2

$$4 y + \frac { 2 } { 5 } y ^ { 2 } + 9 y + \frac { 4 } { 5 } y - y ^ { 2 }$$

Evaluate

$$\frac{3y\left(23-y\right)}{5}$$

Solution Steps

Combine 4y and 9y to get 13y.

$$13y+\frac{2}{5}y^{2}+\frac{4}{5}y-y^{2}$$

Combine 13y and \frac{4}{5}y to get \frac{69}{5}y.

$$\frac{69}{5}y+\frac{2}{5}y^{2}-y^{2}$$

Combine \frac{2}{5}y^{2} and -y^{2} to get -\frac{3}{5}y^{2}.

$$\frac{69}{5}y-\frac{3}{5}y^{2}$$

Factor

$$\frac{3y\left(23-y\right)}{5}$$

Solution Steps

Factor out \frac{1}{5}.

$$\frac{20y+2y^{2}+45y+4y-5y^{2}}{5}$$

Consider 20y+2y^{2}+45y+4y-5y^{2}. Factor out y.

$$y\left(69-3y\right)$$

Consider 20+2y+45+4-5y. Multiply and combine like terms.

$$-3y+69$$

Consider -3y+69. Factor out 3.

$$3\left(-y+23\right)$$

Rewrite the complete factored expression.

$$\frac{3y\left(-y+23\right)}{5}$$