Solve for c square root of 5c+1-10=-6

$\sqrt{5 c + 1} - 10 = - 6$

Move all terms not containing $\sqrt{5 c + 1}$ to the right side of the equation.

Add $10$ to both sides of the equation.

$\sqrt{5 c + 1} = - 6 + 10$

Add $- 6$ and $10$ .

$\sqrt{5 c + 1} = 4$

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

${\sqrt{5 c + 1}}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 c + 1}$ as ${(5 c + 1)}^{\frac{1}{2}}$ .

${({(5 c + 1)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${({(5 c + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 c + 1)}^{\frac{1}{2}})}^{2}$ .

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

${(5 c + 1)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 c + 1)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(5 c + 1)}^{1} = 4^{2}$

Simplify.

$5 c + 1 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$5 c + 1 = 16$

Solve for $c$ .

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

Subtract $1$ from both sides of the equation.

$5 c = 16 - 1$

Subtract $1$ from $16$ .

$5 c = 15$

Divide each term in $5 c = 15$ by $5$ and simplify.

Divide each term in $5 c = 15$ by $5$ .

$\frac{5 c}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 c}{5} = \frac{15}{5}$

Divide $c$ by $1$ .

$c = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$c = 3$