Solve for x 3^(4x-2)=9^(-(x+1))

$3^{4 x - 2} = 9^{- (x + 1)}$

Create equivalent expressions in the equation that all have equal bases.

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

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$4 x - 2 = 2 (- (x + 1))$

Solve for $x$ .

Simplify $2 (- (x + 1))$ .

Rewrite.

$4 x - 2 = 0 + 0 + 2 (- (x + 1))$

Simplify by adding zeros.

$4 x - 2 = 2 (- (x + 1))$

Apply the distributive property.

$4 x - 2 = 2 (- x - 1 \cdot 1)$

Multiply $- 1$ by $1$ .

$4 x - 2 = 2 (- x - 1)$

Apply the distributive property.

$4 x - 2 = 2 (- x) + 2 \cdot - 1$

Multiply.

Multiply $- 1$ by $2$ .

$4 x - 2 = - 2 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$4 x - 2 = - 2 x - 2$

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$4 x - 2 + 2 x = - 2$

Add $4 x$ and $2 x$ .

$6 x - 2 = - 2$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$6 x = - 2 + 2$

Add $- 2$ and $2$ .

$6 x = 0$

Divide each term in $6 x = 0$ by $6$ and simplify.

Divide each term in $6 x = 0$ by $6$ .

$\frac{6 x}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{0}{6}$

Divide $x$ by $1$ .

$x = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

$x = 0$