Solve ax^2+bx+c=5(x-1)(3x-11)

$$a x ^ { 2 } + b x + c = 5 ( x - 1 ) ( 3 x - 11 )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{-15x^{2}+bx+70x+c-55}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=55\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-1.

$$ax^{2}+bx+c=\left(5x-5\right)\left(3x-11\right)$$

Use the distributive property to multiply 5x-5 by 3x-11 and combine like terms.

$$ax^{2}+bx+c=15x^{2}-70x+55$$

Subtract bx from both sides.

$$ax^{2}+c=15x^{2}-70x+55-bx$$

Subtract c from both sides.

$$ax^{2}=15x^{2}-70x+55-bx-c$$

The equation is in standard form.

$$x^{2}a=15x^{2}-bx-70x-c+55$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{15x^{2}-bx-70x-c+55}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{15x^{2}-bx-70x-c+55}{x^{2}}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-ax+15x-\frac{c}{x}-70+\frac{55}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=55\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-1.

$$ax^{2}+bx+c=\left(5x-5\right)\left(3x-11\right)$$

Use the distributive property to multiply 5x-5 by 3x-11 and combine like terms.

$$ax^{2}+bx+c=15x^{2}-70x+55$$

Subtract ax^{2} from both sides.

$$bx+c=15x^{2}-70x+55-ax^{2}$$

Subtract c from both sides.

$$bx=15x^{2}-70x+55-ax^{2}-c$$

Reorder the terms.

$$bx=-ax^{2}+15x^{2}-70x-c+55$$

The equation is in standard form.

$$xb=55-c-70x+15x^{2}-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{55-c-70x+15x^{2}-ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{55-c-70x+15x^{2}-ax^{2}}{x}$$

Divide -ax^{2}+15x^{2}-70x-c+55 by x.

$$b=-ax+15x+\frac{55-c}{x}-70$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{-15x^{2}+bx+70x+c-55}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=55\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-1.

$$ax^{2}+bx+c=\left(5x-5\right)\left(3x-11\right)$$

Use the distributive property to multiply 5x-5 by 3x-11 and combine like terms.

$$ax^{2}+bx+c=15x^{2}-70x+55$$

Subtract bx from both sides.

$$ax^{2}+c=15x^{2}-70x+55-bx$$

Subtract c from both sides.

$$ax^{2}=15x^{2}-70x+55-bx-c$$

The equation is in standard form.

$$x^{2}a=15x^{2}-bx-70x-c+55$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{15x^{2}-bx-70x-c+55}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{15x^{2}-bx-70x-c+55}{x^{2}}$$

Solve for b

$$\left\{\begin{matrix}b=-ax+15x-\frac{c}{x}-70+\frac{55}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=55\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-1.

$$ax^{2}+bx+c=\left(5x-5\right)\left(3x-11\right)$$

Use the distributive property to multiply 5x-5 by 3x-11 and combine like terms.

$$ax^{2}+bx+c=15x^{2}-70x+55$$

Subtract ax^{2} from both sides.

$$bx+c=15x^{2}-70x+55-ax^{2}$$

Subtract c from both sides.

$$bx=15x^{2}-70x+55-ax^{2}-c$$

Reorder the terms.

$$bx=-ax^{2}+15x^{2}-70x-c+55$$

The equation is in standard form.

$$xb=55-c-70x+15x^{2}-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{55-c-70x+15x^{2}-ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{55-c-70x+15x^{2}-ax^{2}}{x}$$

Divide -ax^{2}+15x^{2}-70x-c+55 by x.

$$b=-ax+15x+\frac{55-c}{x}-70$$