(10u^4+5)-(-2u^4+8)=

Solution for (10u^4+5)-(-2u^4+8)= equation:

Simplifying
(10u4 + 5) + -1(-2u4 + 8) = 0

Reorder the terms:
(5 + 10u4) + -1(-2u4 + 8) = 0

Remove parenthesis around (5 + 10u4)
5 + 10u4 + -1(-2u4 + 8) = 0

Reorder the terms:
5 + 10u4 + -1(8 + -2u4) = 0
5 + 10u4 + (8 * -1 + -2u4 * -1) = 0
5 + 10u4 + (-8 + 2u4) = 0

Reorder the terms:
5 + -8 + 10u4 + 2u4 = 0

Combine like terms: 5 + -8 = -3
-3 + 10u4 + 2u4 = 0

Combine like terms: 10u4 + 2u4 = 12u4
-3 + 12u4 = 0

Solving
-3 + 12u4 = 0

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + 12u4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 12u4 = 0 + 3
12u4 = 0 + 3

Combine like terms: 0 + 3 = 3
12u4 = 3

Divide each side by '12'.
u4 = 0.25

Simplifying
u4 = 0.25

Reorder the terms:
-0.25 + u4 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + u4 = 0.00

Factor a difference between two squares.
(0.5 + u2)(-0.5 + u2) = 0.00

Subproblem 1
Set the factor '(0.5 + u2)' equal to zero and attempt to solve:

Simplifying
0.5 + u2 = 0

Solving
0.5 + u2 = 0

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u2 = 0 + -0.5
u2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
u2 = -0.5

Simplifying
u2 = -0.5

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 '(-0.5 + u2)' equal to zero and attempt to solve:

Simplifying
-0.5 + u2 = 0

Solving
-0.5 + u2 = 0

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + u2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + u2 = 0 + 0.5
u2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
u2 = 0.5

Simplifying
u2 = 0.5

Take the square root of each side:
u = {-0.707106781, 0.707106781}
Solution
u = {-0.707106781, 0.707106781}