Solve for c square root of 6c-4=2

$\sqrt{6 c} - 4 = 2$

Step 1

Move all terms not containing $\sqrt{6 c}$ to the right side of the equation.

Add $4$ to both sides of the equation.

$\sqrt{6 c} = 2 + 4$

Add $2$ and $4$ .

$\sqrt{6 c} = 6$

Step 2

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

${\sqrt{6 c}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 c}$ as ${(6 c)}^{\frac{1}{2}}$ .

${({(6 c)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(6 c)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 c)}^{\frac{1}{2}})}^{2}$ .

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

${(6 c)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 c)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(6 c)}^{1} = 6^{2}$

Simplify.

$6 c = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$6 c = 36$

Step 4

Divide each term in $6 c = 36$ by $6$ and simplify.

Divide each term in $6 c = 36$ by $6$ .

$\frac{6 c}{6} = \frac{36}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 c}{6} = \frac{36}{6}$

Divide $c$ by $1$ .

$c = \frac{36}{6}$

Simplify the right side.

Divide $36$ by $6$ .

$c = 6$