u=(2u^2-u+4)+(-5u^2+3u+6)

Solution for u=(2u^2-u+4)+(-5u^2+3u+6) equation:

Simplifying
u = (2u2 + -1u + 4) + (-5u2 + 3u + 6)

Reorder the terms:
u = (4 + -1u + 2u2) + (-5u2 + 3u + 6)

Remove parenthesis around (4 + -1u + 2u2)
u = 4 + -1u + 2u2 + (-5u2 + 3u + 6)

Reorder the terms:
u = 4 + -1u + 2u2 + (6 + 3u + -5u2)

Remove parenthesis around (6 + 3u + -5u2)
u = 4 + -1u + 2u2 + 6 + 3u + -5u2

Reorder the terms:
u = 4 + 6 + -1u + 3u + 2u2 + -5u2

Combine like terms: 4 + 6 = 10
u = 10 + -1u + 3u + 2u2 + -5u2

Combine like terms: -1u + 3u = 2u
u = 10 + 2u + 2u2 + -5u2

Combine like terms: 2u2 + -5u2 = -3u2
u = 10 + 2u + -3u2

Solving
u = 10 + 2u + -3u2

Solving for variable 'u'.

Reorder the terms:
-10 + u + -2u + 3u2 = 10 + 2u + -3u2 + -10 + -2u + 3u2

Combine like terms: u + -2u = -1u
-10 + -1u + 3u2 = 10 + 2u + -3u2 + -10 + -2u + 3u2

Reorder the terms:
-10 + -1u + 3u2 = 10 + -10 + 2u + -2u + -3u2 + 3u2

Combine like terms: 10 + -10 = 0
-10 + -1u + 3u2 = 0 + 2u + -2u + -3u2 + 3u2
-10 + -1u + 3u2 = 2u + -2u + -3u2 + 3u2

Combine like terms: 2u + -2u = 0
-10 + -1u + 3u2 = 0 + -3u2 + 3u2
-10 + -1u + 3u2 = -3u2 + 3u2

Combine like terms: -3u2 + 3u2 = 0
-10 + -1u + 3u2 = 0

Factor a trinomial.
(-5 + -3u)(2 + -1u) = 0

Subproblem 1
Set the factor '(-5 + -3u)' equal to zero and attempt to solve:

Simplifying
-5 + -3u = 0

Solving
-5 + -3u = 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 + -3u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3u = 0 + 5
-3u = 0 + 5

Combine like terms: 0 + 5 = 5
-3u = 5

Divide each side by '-3'.
u = -1.666666667

Simplifying
u = -1.666666667
Subproblem 2
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {-1.666666667, 2}