Solve for b -5(3x^2+5x+b)=ax^2-25x+45

$- 5 (3 x^{2} + 5 x + b) = a x^{2} - 25 x + 45$

Divide each term in $- 5 (3 x^{2} + 5 x + b) = a x^{2} - 25 x + 45$ by $- 5$ and simplify.

Divide each term in $- 5 (3 x^{2} + 5 x + b) = a x^{2} - 25 x + 45$ by $- 5$ .

$\frac{- 5 (3 x^{2} + 5 x + b)}{- 5} = \frac{a x^{2}}{- 5} + \frac{- 25 x}{- 5} + \frac{45}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 (3 x^{2} + 5 x + b)}{- 5} = \frac{a x^{2}}{- 5} + \frac{- 25 x}{- 5} + \frac{45}{- 5}$

Divide $3 x^{2} + 5 x + b$ by $1$ .

$3 x^{2} + 5 x + b = \frac{a x^{2}}{- 5} + \frac{- 25 x}{- 5} + \frac{45}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + \frac{- 25 x}{- 5} + \frac{45}{- 5}$

Cancel the common factor of $- 25$ and $- 5$ .

Factor $- 5$ out of $- 25 x$ .

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + \frac{- 5 (5 x)}{- 5} + \frac{45}{- 5}$

Cancel the common factors.

Factor $- 5$ out of $- 5$ .

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + \frac{- 5 (5 x)}{- 5 (1)} + \frac{45}{- 5}$

Cancel the common factor.

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + \frac{- 5 (5 x)}{- 5 \cdot 1} + \frac{45}{- 5}$

Rewrite the expression.

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + \frac{5 x}{1} + \frac{45}{- 5}$

Divide $5 x$ by $1$ .

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + 5 x + \frac{45}{- 5}$

Divide $45$ by $- 5$ .

$3 x^{2} + 5 x + b = - \frac{a x^{2}}{5} + 5 x - 9$

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

Subtract $3 x^{2}$ from both sides of the equation.

$5 x + b = - \frac{a x^{2}}{5} + 5 x - 9 - 3 x^{2}$

Subtract $5 x$ from both sides of the equation.

$b = - \frac{a x^{2}}{5} + 5 x - 9 - 3 x^{2} - 5 x$

Combine the opposite terms in $- \frac{a x^{2}}{5} + 5 x - 9 - 3 x^{2} - 5 x$ .

Subtract $5 x$ from $5 x$ .

$b = - \frac{a x^{2}}{5} - 9 - 3 x^{2} + 0$

Add $- \frac{a x^{2}}{5} - 9 - 3 x^{2}$ and $0$ .

$b = - \frac{a x^{2}}{5} - 9 - 3 x^{2}$