Solve for y fourth root of 2y+3+1=0

$\sqrt[4]{2 y + 3} + 1 = 0$

Subtract $1$ from both sides of the equation.

$\sqrt[4]{2 y + 3} = - 1$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{2 y + 3}}^{4} = {(- 1)}^{4}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 y + 3}$ as ${(2 y + 3)}^{\frac{1}{4}}$ .

${({(2 y + 3)}^{\frac{1}{4}})}^{4} = {(- 1)}^{4}$

Simplify the left side.

Simplify ${({(2 y + 3)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(2 y + 3)}^{\frac{1}{4}})}^{4}$ .

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

${(2 y + 3)}^{\frac{1}{4} \cdot 4} = {(- 1)}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(2 y + 3)}^{\frac{1}{4} \cdot 4} = {(- 1)}^{4}$

Rewrite the expression.

${(2 y + 3)}^{1} = {(- 1)}^{4}$

Simplify.

$2 y + 3 = {(- 1)}^{4}$

Simplify the right side.

Raise $- 1$ to the power of $4$ .

$2 y + 3 = 1$

Solve for $y$ .

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

Subtract $3$ from both sides of the equation.

$2 y = 1 - 3$

Subtract $3$ from $1$ .

$2 y = - 2$

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

Divide each term in $2 y = - 2$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2}$

Divide $y$ by $1$ .

$y = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$y = - 1$

Exclude the solutions that do not make $\sqrt[4]{2 y + 3} + 1 = 0$ true.

$No solution$