Solve for m square root of 9m+15=6

$\sqrt{9 m} + 15 = 6$

Step 1

Move all terms not containing $\sqrt{9 m}$ to the right side of the equation.

Subtract $15$ from both sides of the equation.

$\sqrt{9 m} = 6 - 15$

Subtract $15$ from $6$ .

$\sqrt{9 m} = - 9$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{9 m}}^{2} = {(- 9)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 m}$ as ${(9 m)}^{\frac{1}{2}}$ .

${({(9 m)}^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Simplify the left side.

Simplify ${({(9 m)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(9 m)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(9 m)}^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9 m)}^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Rewrite the expression.

${(9 m)}^{1} = {(- 9)}^{2}$

Simplify.

$9 m = {(- 9)}^{2}$

Simplify the right side.

Raise $- 9$ to the power of $2$ .

$9 m = 81$

Step 4

Divide each term in $9 m = 81$ by $9$ and simplify.

Divide each term in $9 m = 81$ by $9$ .

$\frac{9 m}{9} = \frac{81}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 m}{9} = \frac{81}{9}$

Divide $m$ by $1$ .

$m = \frac{81}{9}$

Simplify the right side.

Divide $81$ by $9$ .

$m = 9$

Step 5

Exclude the solutions that do not make $\sqrt{9 m} + 15 = 6$ true.

$No solution$