Solve 4ax^2=6ax^2-1ax^2

$$4 a x ^ { 2 } = 6 a x ^ { 2 } - 1 a x ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 6ax^{2} and -ax^{2} to get 5ax^{2}.

$$4ax^{2}=5ax^{2}$$

Subtract 5ax^{2} from both sides.

$$4ax^{2}-5ax^{2}=0$$

Combine 4ax^{2} and -5ax^{2} to get -ax^{2}.

$$-ax^{2}=0$$

The equation is in standard form.

$$\left(-x^{2}\right)a=0$$

Divide 0 by -x^{2}.

$$a=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Steps by Finding Square Root

Combine 6ax^{2} and -ax^{2} to get 5ax^{2}.

$$4ax^{2}=5ax^{2}$$

Subtract 5ax^{2} from both sides.

$$4ax^{2}-5ax^{2}=0$$

Combine 4ax^{2} and -5ax^{2} to get -ax^{2}.

$$-ax^{2}=0$$

Dividing by -a undoes the multiplication by -a.

$$x^{2}=\frac{0}{-a}$$

Divide 0 by -a.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Combine 6ax^{2} and -ax^{2} to get 5ax^{2}.

$$4ax^{2}=5ax^{2}$$

Subtract 5ax^{2} from both sides.

$$4ax^{2}-5ax^{2}=0$$

Combine 4ax^{2} and -5ax^{2} to get -ax^{2}.

$$-ax^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\left(-a\right)x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -a for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2\left(-a\right)}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2\left(-a\right)}$$

Multiply 2 times -a.

$$x=\frac{0}{-2a}$$

Divide 0 by -2a.

$$x=0$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 6ax^{2} and -ax^{2} to get 5ax^{2}.

$$4ax^{2}=5ax^{2}$$

Subtract 5ax^{2} from both sides.

$$4ax^{2}-5ax^{2}=0$$

Combine 4ax^{2} and -5ax^{2} to get -ax^{2}.

$$-ax^{2}=0$$

The equation is in standard form.

$$\left(-x^{2}\right)a=0$$

Divide 0 by -x^{2}.

$$a=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$