Solve sqrt[8]{8}:(x+4)(2x-3)=6

$$\sqrt[ 8 ] { 8 } : ( x + 4 ) ( 2 x - 3 ) = 6$$

Solve for x

$$x = -\frac{3 \cdot 2 ^ {\frac{3}{8}} {(2 \sqrt{2} + 81)} {(4 \cdot 2 ^ {\frac{5}{8}} + 1)} {(2 ^ {\frac{3}{8}} + 3)} {(2 ^ {\frac{3}{4}} + 9)}}{13106} \approx -8.187871771$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x+4.

$$\sqrt[8]{8}\left(2x-3\right)=6\left(x+4\right)$$

Use the distributive property to multiply \sqrt[8]{8} by 2x-3.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}=6\left(x+4\right)$$

Use the distributive property to multiply 6 by x+4.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}=6x+24$$

Subtract 6x from both sides.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}-6x=24$$

Add 3\sqrt[8]{8} to both sides.

$$2\sqrt[8]{8}x-6x=24+3\sqrt[8]{8}$$

Combine all terms containing x.

$$\left(2\sqrt[8]{8}-6\right)x=24+3\sqrt[8]{8}$$

The equation is in standard form.

$$\left(2\sqrt[8]{8}-6\right)x=3\sqrt[8]{8}+24$$

Divide both sides by 2\sqrt[8]{8}-6.

$$\frac{\left(2\sqrt[8]{8}-6\right)x}{2\sqrt[8]{8}-6}=\frac{3\times 2^{\frac{3}{8}}+24}{2\sqrt[8]{8}-6}$$

Dividing by 2\sqrt[8]{8}-6 undoes the multiplication by 2\sqrt[8]{8}-6.

$$x=\frac{3\times 2^{\frac{3}{8}}+24}{2\sqrt[8]{8}-6}$$

Divide 24+3\times 2^{\frac{3}{8}} by 2\sqrt[8]{8}-6.

$$x=-\frac{3\left(2\sqrt{2}+81\right)\left(2^{\frac{3}{8}}+3\right)\left(2^{\frac{3}{4}}+9\right)\left(2^{\frac{7}{8}}+1\right)\sqrt[8]{2}\left(\sqrt[4]{2}+4-2\sqrt[8]{2}\right)}{13106}$$