You need to begin by first factoring the equation to simplest terms.

In your equation x^6 - 7x^3 - 8 =0, start with the term x^6 this can be x^3 * x^3. You would then set up two new parentheses and place x^3 as the first term in each (x^3 + ?)(X^3 + ?)= 0

To determine what goes where the question marks are you need to look for factors of -8 that add to -7.

Factors of -8 sum of factors

1, -8 -7

2, -4 -2

4, -2 2

8, -1 7

From the chart above, you can determine 1, -8.

Your equation is now (x^3 + 1)(x^3 - 8) = 0

You would then set each of these factor equal to zero & solve.

X^3 + 1 = 0 X^3 - 8 = 0

X^3 = -1 X^3 = 8

x = -1 x = 2

To check your answers, substitute the solutions back into the original equation and solve.

x^6 - 7x^3 - 8 = 0

-1^6 -7(-1)^3 - 8 = 0 2^6 - 7(2^3) - 8 = 0

1 + 7-8 = 0 64 - 7(8) - 8 = 0

8-8 = 0 64 - 56 - 8 = 0

0 = 0 checks 0=0 checks