Solve 1/2x(-a^2+2a)*(3-0)=3

$$\frac { 1 } { 2 } x ( - a ^ { 2 } + 2 a ) \times ( 3 - 0 ) = 3$$

Solve for x

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

$$a\neq 2\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Subtract 0 from 3 to get 3.

$$\frac{1}{2}x\left(-a^{2}+2a\right)\times 3=3$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{3}{2}x\left(-a^{2}+2a\right)=3$$

Use the distributive property to multiply \frac{3}{2}x by -a^{2}+2a.

$$\frac{3}{2}x\left(-a^{2}\right)+3xa=3$$

Multiply \frac{3}{2} and -1 to get -\frac{3}{2}.

$$-\frac{3}{2}xa^{2}+3xa=3$$

Combine all terms containing x.

$$\left(-\frac{3}{2}a^{2}+3a\right)x=3$$

The equation is in standard form.

$$\left(-\frac{3a^{2}}{2}+3a\right)x=3$$

Divide both sides by -\frac{3}{2}a^{2}+3a.

$$\frac{\left(-\frac{3a^{2}}{2}+3a\right)x}{-\frac{3a^{2}}{2}+3a}=\frac{3}{-\frac{3a^{2}}{2}+3a}$$

Dividing by -\frac{3}{2}a^{2}+3a undoes the multiplication by -\frac{3}{2}a^{2}+3a.

$$x=\frac{3}{-\frac{3a^{2}}{2}+3a}$$

Divide 3 by -\frac{3}{2}a^{2}+3a.

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

Solve for a (complex solution)

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

$$a=\frac{\sqrt{x\left(x-2\right)}+x}{x}\text{, }x\neq 0$$

Solve for a

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

$$a=\frac{\sqrt{x\left(x-2\right)}+x}{x}\text{, }x<0\text{ or }x\geq 2$$