Solve -5x+(-2^c-3x)-(4x-1)-2x=21

$$- 5 x + ( - 2 ^ { c } - 3 x ) - ( 4 x - 1 ) - 2 x = 21$$

Solve for x

$$x=-\frac{2^{c}}{14}-\frac{10}{7}$$

Steps for Solving Linear Equation

Combine -5x and -3x to get -8x.

$$-8x-2^{c}-\left(4x-1\right)-2x=21$$

To find the opposite of 4x-1, find the opposite of each term.

$$-8x-2^{c}-4x+1-2x=21$$

Combine -8x and -4x to get -12x.

$$-12x-2^{c}+1-2x=21$$

Combine -12x and -2x to get -14x.

$$-14x-2^{c}+1=21$$

Add 2^{c} to both sides.

$$-14x+1=21+2^{c}$$

Subtract 1 from both sides.

$$-14x=21+2^{c}-1$$

Subtract 1 from 21 to get 20.

$$-14x=20+2^{c}$$

The equation is in standard form.

$$-14x=2^{c}+20$$

Divide both sides by -14.

$$\frac{-14x}{-14}=\frac{2^{c}+20}{-14}$$

Dividing by -14 undoes the multiplication by -14.

$$x=\frac{2^{c}+20}{-14}$$

Divide 20+2^{c} by -14.

$$x=-\frac{2^{c}}{14}-\frac{10}{7}$$

Solve for c (complex solution)

$$c=\log_{2}\left(-14x-20\right)+\frac{2\pi n_{1}i}{\ln(2)}$$

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

$$x\neq -\frac{10}{7}$$

Solve for c

$$c=\log_{2}\left(-14x-20\right)$$

$$x<-\frac{10}{7}$$