Solve for s 36^(3s)=216^(2s+1)

$36^{3 s} = 216^{2 s + 1}$

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

$6^{2 (3 s)} = 6^{3 (2 s + 1)}$

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

$2 (3 s) = 3 (2 s + 1)$

Solve for $s$ .

Multiply $3$ by $2$ .

$6 s = 3 (2 s + 1)$

Simplify $3 (2 s + 1)$ .

Apply the distributive property.

$6 s = 3 (2 s) + 3 \cdot 1$

Multiply.

Multiply $2$ by $3$ .

$6 s = 6 s + 3 \cdot 1$

Multiply $3$ by $1$ .

$6 s = 6 s + 3$

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

Subtract $6 s$ from both sides of the equation.

$6 s - 6 s = 3$

Subtract $6 s$ from $6 s$ .

$0 = 3$

Since $0 \neq 3$ , there are no solutions.

No solution