Solve 6x^2-13x+z=0z==

$$6 { x }^{ 2 } -13x+z=0z==$$

Solve for z

$$z=-x\left(6x-13\right)$$

Solution Steps

Anything times zero gives zero.

$$6x^{2}-13x+z=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-13x+z=-6x^{2}$$

Add 13x to both sides.

$$z=-6x^{2}+13x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{169-24z}+13}{12}$$

$$x=\frac{-\sqrt{169-24z}+13}{12}$$

Solve for x

$$x=\frac{\sqrt{169-24z}+13}{12}$$

$$x=\frac{-\sqrt{169-24z}+13}{12}\text{, }z\leq \frac{169}{24}$$