Solve B=2ax^2-5ax^2+ax^2

$$B = 2 a x ^ { 2 } - 5 a x ^ { 2 } + a x ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{B}{2x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&B=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2ax^{2} and -5ax^{2} to get -3ax^{2}.

$$B=-3ax^{2}+ax^{2}$$

Combine -3ax^{2} and ax^{2} to get -2ax^{2}.

$$B=-2ax^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-2ax^{2}=B$$

The equation is in standard form.

$$\left(-2x^{2}\right)a=B$$

Divide both sides by -2x^{2}.

$$\frac{\left(-2x^{2}\right)a}{-2x^{2}}=\frac{B}{-2x^{2}}$$

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

$$a=\frac{B}{-2x^{2}}$$

Divide B by -2x^{2}.

$$a=-\frac{B}{2x^{2}}$$

Solve for B

$$B=-2ax^{2}$$

Solution Steps

Combine 2ax^{2} and -5ax^{2} to get -3ax^{2}.

$$B=-3ax^{2}+ax^{2}$$

Combine -3ax^{2} and ax^{2} to get -2ax^{2}.

$$B=-2ax^{2}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{B}{2x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&B=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2ax^{2} and -5ax^{2} to get -3ax^{2}.

$$B=-3ax^{2}+ax^{2}$$

Combine -3ax^{2} and ax^{2} to get -2ax^{2}.

$$B=-2ax^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-2ax^{2}=B$$

The equation is in standard form.

$$\left(-2x^{2}\right)a=B$$

Divide both sides by -2x^{2}.

$$\frac{\left(-2x^{2}\right)a}{-2x^{2}}=\frac{B}{-2x^{2}}$$

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

$$a=\frac{B}{-2x^{2}}$$

Divide B by -2x^{2}.

$$a=-\frac{B}{2x^{2}}$$