10u^4-7u^2-45=0

Solution for 10u^4-7u^2-45=0 equation:

Simplifying
10u4 + -7u2 + -45 = 0

Reorder the terms:
-45 + -7u2 + 10u4 = 0

Solving
-45 + -7u2 + 10u4 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + -5u2)(5 + -2u2) = 0

Subproblem 1
Set the factor '(-9 + -5u2)' equal to zero and attempt to solve:

Simplifying
-9 + -5u2 = 0

Solving
-9 + -5u2 = 0

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

Add '9' to each side of the equation.
-9 + 9 + -5u2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5u2 = 0 + 9
-5u2 = 0 + 9

Combine like terms: 0 + 9 = 9
-5u2 = 9

Divide each side by '-5'.
u2 = -1.8

Simplifying
u2 = -1.8

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 '(5 + -2u2)' equal to zero and attempt to solve:

Simplifying
5 + -2u2 = 0

Solving
5 + -2u2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2u2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2u2 = 0 + -5
-2u2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2u2 = -5

Divide each side by '-2'.
u2 = 2.5

Simplifying
u2 = 2.5

Take the square root of each side:
u = {-1.58113883, 1.58113883}
Solution
u = {-1.58113883, 1.58113883}