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

$$3 x ^ { 2 } - 2 ( a + 3 ) x + 3 a = 0$$

Solve for a

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

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Multiply -1 and 2 to get -2.

$$3x^{2}-2\left(a+3\right)x+3a=0$$

Use the distributive property to multiply -2 by a+3.

$$3x^{2}+\left(-2a-6\right)x+3a=0$$

Use the distributive property to multiply -2a-6 by x.

$$3x^{2}-2ax-6x+3a=0$$

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2ax-6x+3a=-3x^{2}$$

Add 6x to both sides.

$$-2ax+3a=-3x^{2}+6x$$

Combine all terms containing a.

$$\left(-2x+3\right)a=-3x^{2}+6x$$

The equation is in standard form.

$$\left(3-2x\right)a=6x-3x^{2}$$

Divide both sides by -2x+3.

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

Dividing by -2x+3 undoes the multiplication by -2x+3.

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

Solve for x

$$x=\frac{\sqrt{a^{2}-3a+9}+a+3}{3}$$

$$x=\frac{-\sqrt{a^{2}-3a+9}+a+3}{3}$$