Solve for x 6^(2x+5)-36=0

$6^{2 x + 5} - 36 = 0$

Add $36$ to both sides of the equation.

$6^{2 x + 5} = 36$

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

$6^{2 x + 5} = 6^{2}$

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

$2 x + 5 = 2$

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$2 x = 2 - 5$

Subtract $5$ from $2$ .

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{2}$

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$