Solve for x -2(3x+4)^(1/2)-3=21

$- 2 {(3 x + 4)}^{\frac{1}{2}} - 3 = 21$

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

Add $3$ to both sides of the equation.

$- 2 {(3 x + 4)}^{\frac{1}{2}} = 21 + 3$

Add $21$ and $3$ .

$- 2 {(3 x + 4)}^{\frac{1}{2}} = 24$

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(- 2 {(3 x + 4)}^{\frac{1}{2}})}^{2} = 24^{2}$

Simplify the exponent.

Simplify the left side.

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

Apply the product rule to $- 2 {(3 x + 4)}^{\frac{1}{2}}$ .

${(- 2)}^{2} {({(3 x + 4)}^{\frac{1}{2}})}^{2} = 24^{2}$

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

$4 {({(3 x + 4)}^{\frac{1}{2}})}^{2} = 24^{2}$

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

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

$4 {(3 x + 4)}^{\frac{1}{2} \cdot 2} = 24^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(3 x + 4)}^{\frac{1}{2} \cdot 2} = 24^{2}$

Rewrite the expression.

$4 {(3 x + 4)}^{1} = 24^{2}$

Simplify.

$4 (3 x + 4) = 24^{2}$

Apply the distributive property.

$4 (3 x) + 4 \cdot 4 = 24^{2}$

Multiply.

Multiply $3$ by $4$ .

$12 x + 4 \cdot 4 = 24^{2}$

Multiply $4$ by $4$ .

$12 x + 16 = 24^{2}$

Simplify the right side.

Raise $24$ to the power of $2$ .

$12 x + 16 = 576$

Solve for $x$ .

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

Subtract $16$ from both sides of the equation.

$12 x = 576 - 16$

Subtract $16$ from $576$ .

$12 x = 560$

Divide each term in $12 x = 560$ by $12$ and simplify.

Divide each term in $12 x = 560$ by $12$ .

$\frac{12 x}{12} = \frac{560}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{560}{12}$

Divide $x$ by $1$ .

$x = \frac{560}{12}$

Simplify the right side.

Cancel the common factor of $560$ and $12$ .

Factor $4$ out of $560$ .

$x = \frac{4 (140)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 140}{4 \cdot 3}$

Cancel the common factor.

$x = \frac{4 \cdot 140}{4 \cdot 3}$

Rewrite the expression.

$x = \frac{140}{3}$

Exclude the solutions that do not make $- 2 {(3 x + 4)}^{\frac{1}{2}} - 3 = 21$ true.

$No solution$

Solve for x -2(3x+4)^(1/2)-3=21

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