Solve for b 7(ay^2+by-3)=14y^2-7y-21

$7 (a y^{2} + b y - 3) = 14 y^{2} - 7 y - 21$

Step 1

Divide each term in $7 (a y^{2} + b y - 3) = 14 y^{2} - 7 y - 21$ by $7$ and simplify.

Divide each term in $7 (a y^{2} + b y - 3) = 14 y^{2} - 7 y - 21$ by $7$ .

$\frac{7 (a y^{2} + b y - 3)}{7} = \frac{14 y^{2}}{7} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (a y^{2} + b y - 3)}{7} = \frac{14 y^{2}}{7} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Divide $a y^{2} + b y - 3$ by $1$ .

$a y^{2} + b y - 3 = \frac{14 y^{2}}{7} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $14$ and $7$ .

Factor $7$ out of $14 y^{2}$ .

$a y^{2} + b y - 3 = \frac{7 (2 y^{2})}{7} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Cancel the common factors.

Factor $7$ out of $7$ .

$a y^{2} + b y - 3 = \frac{7 (2 y^{2})}{7 (1)} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Cancel the common factor.

$a y^{2} + b y - 3 = \frac{7 (2 y^{2})}{7 \cdot 1} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Rewrite the expression.

$a y^{2} + b y - 3 = \frac{2 y^{2}}{1} + \frac{- 7 y}{7} + \frac{- 21}{7}$

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

$a y^{2} + b y - 3 = 2 y^{2} + \frac{- 7 y}{7} + \frac{- 21}{7}$

Cancel the common factor of $- 7$ and $7$ .

Factor $7$ out of $- 7 y$ .

$a y^{2} + b y - 3 = 2 y^{2} + \frac{7 (- y)}{7} + \frac{- 21}{7}$

Cancel the common factors.

Factor $7$ out of $7$ .

$a y^{2} + b y - 3 = 2 y^{2} + \frac{7 (- y)}{7 (1)} + \frac{- 21}{7}$

Cancel the common factor.

$a y^{2} + b y - 3 = 2 y^{2} + \frac{7 (- y)}{7 \cdot 1} + \frac{- 21}{7}$

Rewrite the expression.

$a y^{2} + b y - 3 = 2 y^{2} + \frac{- y}{1} + \frac{- 21}{7}$

Divide $- y$ by $1$ .

$a y^{2} + b y - 3 = 2 y^{2} - y + \frac{- 21}{7}$

Divide $- 21$ by $7$ .

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

Step 2

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

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

$b y - 3 = 2 y^{2} - y - 3 - a y^{2}$

Add $3$ to both sides of the equation.

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

Combine the opposite terms in $2 y^{2} - y - 3 - a y^{2} + 3$ .

Add $- 3$ and $3$ .

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

Add $2 y^{2} - y - a y^{2}$ and $0$ .

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 y$ by $1$ .

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

Cancel the common factor of $y$ .

Cancel the common factor.

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

Divide $- 1$ by $1$ .

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

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

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- a y$ by $1$ .

$b = 2 y - 1 - a y$

Solve for b 7(ay^2+by-3)=14y^2-7y-21

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