Solve for p 2(12p+28)^(1/4)-15=-7

$2 {(12 p + 28)}^{\frac{1}{4}} - 15 = - 7$

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

Add $15$ to both sides of the equation.

$2 {(12 p + 28)}^{\frac{1}{4}} = - 7 + 15$

Add $- 7$ and $15$ .

$2 {(12 p + 28)}^{\frac{1}{4}} = 8$

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

${(2 {(12 p + 28)}^{\frac{1}{4}})}^{4} = 8^{4}$

Simplify the exponent.

Simplify the left side.

Simplify ${(2 {(12 p + 28)}^{\frac{1}{4}})}^{4}$ .

Apply the product rule to $2 {(12 p + 28)}^{\frac{1}{4}}$ .

$2^{4} {({(12 p + 28)}^{\frac{1}{4}})}^{4} = 8^{4}$

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

$16 {({(12 p + 28)}^{\frac{1}{4}})}^{4} = 8^{4}$

Multiply the exponents in ${({(12 p + 28)}^{\frac{1}{4}})}^{4}$ .

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

$16 {(12 p + 28)}^{\frac{1}{4} \cdot 4} = 8^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$16 {(12 p + 28)}^{\frac{1}{4} \cdot 4} = 8^{4}$

Rewrite the expression.

$16 {(12 p + 28)}^{1} = 8^{4}$

Simplify.

$16 (12 p + 28) = 8^{4}$

Apply the distributive property.

$16 (12 p) + 16 \cdot 28 = 8^{4}$

Multiply.

Multiply $12$ by $16$ .

$192 p + 16 \cdot 28 = 8^{4}$

Multiply $16$ by $28$ .

$192 p + 448 = 8^{4}$

Simplify the right side.

Raise $8$ to the power of $4$ .

$192 p + 448 = 4096$

Solve for $p$ .

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

Subtract $448$ from both sides of the equation.

$192 p = 4096 - 448$

Subtract $448$ from $4096$ .

$192 p = 3648$

Divide each term in $192 p = 3648$ by $192$ and simplify.

Divide each term in $192 p = 3648$ by $192$ .

$\frac{192 p}{192} = \frac{3648}{192}$

Simplify the left side.

Cancel the common factor of $192$ .

Cancel the common factor.

$\frac{192 p}{192} = \frac{3648}{192}$

Divide $p$ by $1$ .

$p = \frac{3648}{192}$

Simplify the right side.

Divide $3648$ by $192$ .

$p = 19$

Solve for p 2(12p+28)^(1/4)-15=-7

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