Solve for a (8x^2-15x)-(x^2-27x)=ax^2+bx

$(8 x^{2} - 15 x) - (x^{2} - 27 x) = a x^{2} + b x$

Rewrite the equation as $a x^{2} + b x = 8 x^{2} - 15 x - (x^{2} - 27 x)$ .

$a x^{2} + b x = 8 x^{2} - 15 x - (x^{2} - 27 x)$

Simplify $8 x^{2} - 15 x - (x^{2} - 27 x)$ .

Simplify each term.

Apply the distributive property.

$a x^{2} + b x = 8 x^{2} - 15 x - x^{2} - (- 27 x)$

Multiply $- 27$ by $- 1$ .

$a x^{2} + b x = 8 x^{2} - 15 x - x^{2} + 27 x$

Simplify by adding terms.

Subtract $x^{2}$ from $8 x^{2}$ .

$a x^{2} + b x = 7 x^{2} - 15 x + 27 x$

Add $- 15 x$ and $27 x$ .

$a x^{2} + b x = 7 x^{2} + 12 x$

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

$a x^{2} = 7 x^{2} + 12 x - b x$

Divide each term in $a x^{2} = 7 x^{2} + 12 x - b x$ by $x^{2}$ and simplify.

Divide each term in $a x^{2} = 7 x^{2} + 12 x - b x$ by $x^{2}$ .

$\frac{a x^{2}}{x^{2}} = \frac{7 x^{2}}{x^{2}} + \frac{12 x}{x^{2}} + \frac{- b x}{x^{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{a x^{2}}{x^{2}} = \frac{7 x^{2}}{x^{2}} + \frac{12 x}{x^{2}} + \frac{- b x}{x^{2}}$

Divide $a$ by $1$ .

$a = \frac{7 x^{2}}{x^{2}} + \frac{12 x}{x^{2}} + \frac{- b x}{x^{2}}$

Simplify the right side.

Simplify each term.

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

Cancel the common factor.

$a = \frac{7 x^{2}}{x^{2}} + \frac{12 x}{x^{2}} + \frac{- b x}{x^{2}}$

Divide $7$ by $1$ .

$a = 7 + \frac{12 x}{x^{2}} + \frac{- b x}{x^{2}}$

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

Factor $x$ out of $12 x$ .

$a = 7 + \frac{x \cdot 12}{x^{2}} + \frac{- b x}{x^{2}}$

Cancel the common factors.

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

$a = 7 + \frac{x \cdot 12}{x \cdot x} + \frac{- b x}{x^{2}}$

Cancel the common factor.

$a = 7 + \frac{x \cdot 12}{x \cdot x} + \frac{- b x}{x^{2}}$

Rewrite the expression.

$a = 7 + \frac{12}{x} + \frac{- b x}{x^{2}}$

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

Factor $x$ out of $- b x$ .

$a = 7 + \frac{12}{x} + \frac{x (- b)}{x^{2}}$

Cancel the common factors.

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

$a = 7 + \frac{12}{x} + \frac{x (- b)}{x \cdot x}$

Cancel the common factor.

$a = 7 + \frac{12}{x} + \frac{x (- b)}{x \cdot x}$

Rewrite the expression.

$a = 7 + \frac{12}{x} + \frac{- b}{x}$

Move the negative in front of the fraction.

$a = 7 + \frac{12}{x} - \frac{b}{x}$

Solve for a (8x^2-15x)-(x^2-27x)=ax^2+bx

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