Solve for a -11(y^2-ay+2)=-11y^2+33y-b

$- 11 (y^{2} - a y + 2) = - 11 y^{2} + 33 y - b$

Divide each term in $- 11 (y^{2} - a y + 2) = - 11 y^{2} + 33 y - b$ by $- 11$ and simplify.

Divide each term in $- 11 (y^{2} - a y + 2) = - 11 y^{2} + 33 y - b$ by $- 11$ .

$\frac{- 11 (y^{2} - a y + 2)}{- 11} = \frac{- 11 y^{2}}{- 11} + \frac{33 y}{- 11} + \frac{- b}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 (y^{2} - a y + 2)}{- 11} = \frac{- 11 y^{2}}{- 11} + \frac{33 y}{- 11} + \frac{- b}{- 11}$

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

$y^{2} - a y + 2 = \frac{- 11 y^{2}}{- 11} + \frac{33 y}{- 11} + \frac{- b}{- 11}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$y^{2} - a y + 2 = \frac{- 11 y^{2}}{- 11} + \frac{33 y}{- 11} + \frac{- b}{- 11}$

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

$y^{2} - a y + 2 = y^{2} + \frac{33 y}{- 11} + \frac{- b}{- 11}$

Cancel the common factor of $33$ and $- 11$ .

Factor $11$ out of $33 y$ .

$y^{2} - a y + 2 = y^{2} + \frac{11 (3 y)}{- 11} + \frac{- b}{- 11}$

Move the negative one from the denominator of $\frac{3 y}{- 1}$ .

$y^{2} - a y + 2 = y^{2} - 1 \cdot (3 y) + \frac{- b}{- 11}$

Rewrite $- 1 \cdot (3 y)$ as $- (3 y)$ .

$y^{2} - a y + 2 = y^{2} - (3 y) + \frac{- b}{- 11}$

Multiply $3$ by $- 1$ .

$y^{2} - a y + 2 = y^{2} - 3 y + \frac{- b}{- 11}$

Dividing two negative values results in a positive value.

$y^{2} - a y + 2 = y^{2} - 3 y + \frac{b}{11}$

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

Subtract $y^{2}$ from both sides of the equation.

$- a y + 2 = y^{2} - 3 y + \frac{b}{11} - y^{2}$

Subtract $2$ from both sides of the equation.

$- a y = y^{2} - 3 y + \frac{b}{11} - y^{2} - 2$

Combine the opposite terms in $y^{2} - 3 y + \frac{b}{11} - y^{2} - 2$ .

Subtract $y^{2}$ from $y^{2}$ .

$- a y = - 3 y + \frac{b}{11} + 0 - 2$

Add $- 3 y + \frac{b}{11}$ and $0$ .

$- a y = - 3 y + \frac{b}{11} - 2$

Divide each term in $- a y = - 3 y + \frac{b}{11} - 2$ by $- 1 y$ and simplify.

Divide each term in $- a y = - 3 y + \frac{b}{11} - 2$ by $- 1 y$ .

$\frac{- a y}{- 1 y} = \frac{- 3 y}{- 1 y} + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{a y}{y} = \frac{- 3 y}{- 1 y} + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{a y}{y} = \frac{- 3 y}{- 1 y} + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Divide $a$ by $1$ .

$a = \frac{- 3 y}{- 1 y} + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $y$ .

Cancel the common factor.

$a = \frac{- 3 y}{- 1 y} + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Rewrite the expression.

$a = \frac{- 3}{- 1} + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Move the negative one from the denominator of $\frac{- 3}{- 1}$ .

$a = - 1 \cdot - 3 + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Rewrite $- 1 \cdot - 3$ as $- - 3$ .

$a = - - 3 + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Multiply $- 1$ by $- 3$ .

$a = 3 + \frac{\frac{b}{11}}{- 1 y} + \frac{- 2}{- 1 y}$

Multiply the numerator by the reciprocal of the denominator.

$a = 3 + \frac{b}{11} \cdot \frac{1}{- 1 y} + \frac{- 2}{- 1 y}$

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$a = 3 + \frac{b}{11} \cdot \frac{- 1 (- 1)}{- 1 y} + \frac{- 2}{- 1 y}$

Move the negative in front of the fraction.

$a = 3 + \frac{b}{11} (- \frac{1}{y}) + \frac{- 2}{- 1 y}$

Rewrite using the commutative property of multiplication.

$a = 3 - \frac{b}{11} \cdot \frac{1}{y} + \frac{- 2}{- 1 y}$

Multiply $\frac{1}{y}$ by $\frac{b}{11}$ .

$a = 3 - \frac{b}{y \cdot 11} + \frac{- 2}{- 1 y}$

Move $11$ to the left of $y$ .

$a = 3 - \frac{b}{11 \cdot y} + \frac{- 2}{- 1 y}$

Dividing two negative values results in a positive value.

$a = 3 - \frac{b}{11 y} + \frac{2}{y}$

Solve for a -11(y^2-ay+2)=-11y^2+33y-b

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