Solve ax^5+bx^4+cx^3+dx^2+ex+f=0

$$a x ^ { 5 } + b x ^ { 4 } + c x ^ { 3 } + d x ^ { 2 } + e x + f = 0$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx^{4}+cx^{3}+dx^{2}+ex+f}{x^{5}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx^{4} from both sides. Anything subtracted from zero gives its negation.

$$ax^{5}+cx^{3}+dx^{2}+ex+f=-bx^{4}$$

Subtract cx^{3} from both sides.

$$ax^{5}+dx^{2}+ex+f=-bx^{4}-cx^{3}$$

Subtract dx^{2} from both sides.

$$ax^{5}+ex+f=-bx^{4}-cx^{3}-dx^{2}$$

Subtract ex from both sides.

$$ax^{5}+f=-bx^{4}-cx^{3}-dx^{2}-ex$$

Subtract f from both sides.

$$ax^{5}=-bx^{4}-cx^{3}-dx^{2}-ex-f$$

The equation is in standard form.

$$x^{5}a=-bx^{4}-cx^{3}-dx^{2}-ex-f$$

Divide both sides by x^{5}.

$$\frac{x^{5}a}{x^{5}}=\frac{-bx^{4}-cx^{3}-dx^{2}-ex-f}{x^{5}}$$

Dividing by x^{5} undoes the multiplication by x^{5}.

$$a=\frac{-bx^{4}-cx^{3}-dx^{2}-ex-f}{x^{5}}$$

Divide -bx^{4}-cx^{3}-dx^{2}-ex-f by x^{5}.

$$a=-\frac{bx^{4}+cx^{3}+dx^{2}+ex+f}{x^{5}}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ax^{5}+cx^{3}+dx^{2}+ex+f}{x^{4}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ax^{5} from both sides. Anything subtracted from zero gives its negation.

$$bx^{4}+cx^{3}+dx^{2}+ex+f=-ax^{5}$$

Subtract cx^{3} from both sides.

$$bx^{4}+dx^{2}+ex+f=-ax^{5}-cx^{3}$$

Subtract dx^{2} from both sides.

$$bx^{4}+ex+f=-ax^{5}-cx^{3}-dx^{2}$$

Subtract ex from both sides.

$$bx^{4}+f=-ax^{5}-cx^{3}-dx^{2}-ex$$

Subtract f from both sides.

$$bx^{4}=-ax^{5}-cx^{3}-dx^{2}-ex-f$$

The equation is in standard form.

$$x^{4}b=-ax^{5}-cx^{3}-dx^{2}-ex-f$$

Divide both sides by x^{4}.

$$\frac{x^{4}b}{x^{4}}=\frac{-ax^{5}-cx^{3}-dx^{2}-ex-f}{x^{4}}$$

Dividing by x^{4} undoes the multiplication by x^{4}.

$$b=\frac{-ax^{5}-cx^{3}-dx^{2}-ex-f}{x^{4}}$$

Divide -ax^{5}-cx^{3}-dx^{2}-ex-f by x^{4}.

$$b=-ax-\frac{cx^{3}+dx^{2}+ex+f}{x^{4}}$$