Solve 6^x-4(2)(-3+2k)=0

$$6 ^ { x } - 4 ( 2 ) ( - 3 + 2 k ) = 0$$

Solve for k

$$k=\frac{6^{x}+24}{16}$$

Steps for Solving Linear Equation

Multiply 4 and 2 to get 8.

$$6^{x}-8\left(-3+2k\right)=0$$

Use the distributive property to multiply -8 by -3+2k.

$$6^{x}+24-16k=0$$

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

$$24-16k=-6^{x}$$

Subtract 24 from both sides.

$$-16k=-6^{x}-24$$

Divide both sides by -16.

$$\frac{-16k}{-16}=\frac{-6^{x}-24}{-16}$$

Dividing by -16 undoes the multiplication by -16.

$$k=\frac{-6^{x}-24}{-16}$$

Divide -6^{x}-24 by -16.

$$k=\frac{6^{x}}{16}+\frac{3}{2}$$

Solve for x (complex solution)

$$x=\log_{6}\left(16k-24\right)+\frac{2\pi n_{1}i}{\ln(6)}$$

$$n_{1}\in \mathrm{Z}$$

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

Solve for x

$$x=\log_{6}\left(16k-24\right)$$

$$k>\frac{3}{2}$$