7x^8+3x^4-10=0

Solution for 7x^8+3x^4-10=0 equation:

Simplifying
7x8 + 3x4 + -10 = 0

Reorder the terms:
-10 + 3x4 + 7x8 = 0

Solving
-10 + 3x4 + 7x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -7x4)(1 + -1x4) = 0

Factor a difference between two squares.
(-10 + -7x4)((1 + x2)(1 + -1x2)) = 0

Factor a difference between two squares.
(-10 + -7x4)((1 + x2)((1 + x)(1 + -1x))) = 0

Subproblem 1
Set the factor '(-10 + -7x4)' equal to zero and attempt to solve:

Simplifying
-10 + -7x4 = 0

Solving
-10 + -7x4 = 0

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + -7x4 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7x4 = 0 + 10
-7x4 = 0 + 10

Combine like terms: 0 + 10 = 10
-7x4 = 10

Divide each side by '-7'.
x4 = -1.428571429

Simplifying
x4 = -1.428571429

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1, 1}