Solve for a 4y(ay^2-7y+b)=24y^3-28y^2-8y

$4 y (a y^{2} - 7 y + b) = 24 y^{3} - 28 y^{2} - 8 y$

Divide each term in $4 y (a y^{2} - 7 y + b) = 24 y^{3} - 28 y^{2} - 8 y$ by $4 y$ and simplify.

Divide each term in $4 y (a y^{2} - 7 y + b) = 24 y^{3} - 28 y^{2} - 8 y$ by $4 y$ .

$\frac{4 y (a y^{2} - 7 y + b)}{4 y} = \frac{24 y^{3}}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y (a y^{2} - 7 y + b)}{4 y} = \frac{24 y^{3}}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Rewrite the expression.

$\frac{y (a y^{2} - 7 y + b)}{y} = \frac{24 y^{3}}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y (a y^{2} - 7 y + b)}{y} = \frac{24 y^{3}}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Divide $a y^{2} - 7 y + b$ by $1$ .

$a y^{2} - 7 y + b = \frac{24 y^{3}}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $24$ and $4$ .

Factor $4$ out of $24 y^{3}$ .

$a y^{2} - 7 y + b = \frac{4 (6 y^{3})}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factors.

Factor $4$ out of $4 y$ .

$a y^{2} - 7 y + b = \frac{4 (6 y^{3})}{4 (y)} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factor.

$a y^{2} - 7 y + b = \frac{4 (6 y^{3})}{4 y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Rewrite the expression.

$a y^{2} - 7 y + b = \frac{6 y^{3}}{y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factor of $y^{3}$ and $y$ .

Factor $y$ out of $6 y^{3}$ .

$a y^{2} - 7 y + b = \frac{y (6 y^{2})}{y} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$a y^{2} - 7 y + b = \frac{y (6 y^{2})}{y^{1}} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Factor $y$ out of $y^{1}$ .

$a y^{2} - 7 y + b = \frac{y (6 y^{2})}{y \cdot 1} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factor.

$a y^{2} - 7 y + b = \frac{y (6 y^{2})}{y \cdot 1} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Rewrite the expression.

$a y^{2} - 7 y + b = \frac{6 y^{2}}{1} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Divide $6 y^{2}$ by $1$ .

$a y^{2} - 7 y + b = 6 y^{2} + \frac{- 28 y^{2}}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factor of $- 28$ and $4$ .

Factor $4$ out of $- 28 y^{2}$ .

$a y^{2} - 7 y + b = 6 y^{2} + \frac{4 (- 7 y^{2})}{4 y} + \frac{- 8 y}{4 y}$

Cancel the common factors.

Factor $4$ out of $4 y$ .

$a y^{2} - 7 y + b = 6 y^{2} + \frac{4 (- 7 y^{2})}{4 (y)} + \frac{- 8 y}{4 y}$

Cancel the common factor.

$a y^{2} - 7 y + b = 6 y^{2} + \frac{4 (- 7 y^{2})}{4 y} + \frac{- 8 y}{4 y}$

Rewrite the expression.

$a y^{2} - 7 y + b = 6 y^{2} + \frac{- 7 y^{2}}{y} + \frac{- 8 y}{4 y}$

Cancel the common factor of $y^{2}$ and $y$ .

Factor $y$ out of $- 7 y^{2}$ .

$a y^{2} - 7 y + b = 6 y^{2} + \frac{y (- 7 y)}{y} + \frac{- 8 y}{4 y}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$a y^{2} - 7 y + b = 6 y^{2} + \frac{y (- 7 y)}{y^{1}} + \frac{- 8 y}{4 y}$

Factor $y$ out of $y^{1}$ .

$a y^{2} - 7 y + b = 6 y^{2} + \frac{y (- 7 y)}{y \cdot 1} + \frac{- 8 y}{4 y}$

Cancel the common factor.

$a y^{2} - 7 y + b = 6 y^{2} + \frac{y (- 7 y)}{y \cdot 1} + \frac{- 8 y}{4 y}$

Rewrite the expression.

$a y^{2} - 7 y + b = 6 y^{2} + \frac{- 7 y}{1} + \frac{- 8 y}{4 y}$

Divide $- 7 y$ by $1$ .

$a y^{2} - 7 y + b = 6 y^{2} - 7 y + \frac{- 8 y}{4 y}$

Cancel the common factor of $- 8$ and $4$ .

Factor $4$ out of $- 8 y$ .

$a y^{2} - 7 y + b = 6 y^{2} - 7 y + \frac{4 (- 2 y)}{4 y}$

Cancel the common factors.

Factor $4$ out of $4 y$ .

$a y^{2} - 7 y + b = 6 y^{2} - 7 y + \frac{4 (- 2 y)}{4 (y)}$

Cancel the common factor.

$a y^{2} - 7 y + b = 6 y^{2} - 7 y + \frac{4 (- 2 y)}{4 y}$

Rewrite the expression.

$a y^{2} - 7 y + b = 6 y^{2} - 7 y + \frac{- 2 y}{y}$

Cancel the common factor of $y$ .

Cancel the common factor.

$a y^{2} - 7 y + b = 6 y^{2} - 7 y + \frac{- 2 y}{y}$

Divide $- 2$ by $1$ .

$a y^{2} - 7 y + b = 6 y^{2} - 7 y - 2$

Move all terms not containing $a$ to the right side of the equation.

Add $7 y$ to both sides of the equation.

$a y^{2} + b = 6 y^{2} - 7 y - 2 + 7 y$

Subtract $b$ from both sides of the equation.

$a y^{2} = 6 y^{2} - 7 y - 2 + 7 y - b$

Combine the opposite terms in $6 y^{2} - 7 y - 2 + 7 y - b$ .

Add $- 7 y$ and $7 y$ .

$a y^{2} = 6 y^{2} + 0 - 2 - b$

Add $6 y^{2}$ and $0$ .

$a y^{2} = 6 y^{2} - 2 - b$

Divide each term in $a y^{2} = 6 y^{2} - 2 - b$ by $y^{2}$ and simplify.

Divide each term in $a y^{2} = 6 y^{2} - 2 - b$ by $y^{2}$ .

$\frac{a y^{2}}{y^{2}} = \frac{6 y^{2}}{y^{2}} + \frac{- 2}{y^{2}} + \frac{- b}{y^{2}}$

Simplify the left side.

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

$\frac{a y^{2}}{y^{2}} = \frac{6 y^{2}}{y^{2}} + \frac{- 2}{y^{2}} + \frac{- b}{y^{2}}$

Divide $a$ by $1$ .

$a = \frac{6 y^{2}}{y^{2}} + \frac{- 2}{y^{2}} + \frac{- b}{y^{2}}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

$a = \frac{6 y^{2}}{y^{2}} + \frac{- 2}{y^{2}} + \frac{- b}{y^{2}}$

Divide $6$ by $1$ .

$a = 6 + \frac{- 2}{y^{2}} + \frac{- b}{y^{2}}$

Move the negative in front of the fraction.

$a = 6 - \frac{2}{y^{2}} + \frac{- b}{y^{2}}$

Move the negative in front of the fraction.

$a = 6 - \frac{2}{y^{2}} - \frac{b}{y^{2}}$

Solve for a 4y(ay^2-7y+b)=24y^3-28y^2-8y

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